Vector addition Definition and 183 Threads

Homework Statement Let V be the set of all ordered pairs of real numbers. Suppose we define addition and scalar multiplication of elements of V in an unusual way so that when u=(x1, y1), v=(x2, y2) and k∈ℝ u+v= (x1⋅x2, y1+y2) and k⋅u=(x1/k, y1/k) Show detailed calculations of one case...

Homework Statement A car is driven 225 km west and then 98 km southwest (45 degrees). What is the displacement of the car from the point (magnitude and direction)? Draw a diagram. Homework Equations Vectors have magnitude and direction. The Attempt at a Solution My attempt is attached. This...

The teacher does not want this homework back, I just want to learn because I love science "1) A golf ball at a mini golf course is hit 10m NE where it hits a barrier and travels NW for another 18m. What is the balls displacement from the tee?" square root(18^2)+(10^2)= 20.6 metres. Now for the...

Hello, here is a couple of example problems I'm not sure how to do, if someone could please explain how to do it I would greatly appreciate it! Subtraction: "A river flows at 0.8 m/s. If a boat moves across the water at 2m/s at what angle should it point so that it moves straight across the...

Homework Statement [/B] The block shown in Fig. P-223 is acted upon by its weight W = 200lb, a horizontal force Q = 600lb and the pressure P exerted by the inclined plane. The resultant R of these forces is up and parallel to the incline thereby sliding the block up it. Determine P and R. Hint...

Homework Statement FC of magnitude 188 N. Note that the direction of FC is not given. What is the magnitude of Betty's force FB if Charles pulls in (a) the direction drawn in the picture or (b) the other possible direction for equilibrium Homework Equations ΣF=0[/B]The Attempt at a Solution...

Question is regarding Scalars and Vectors Article. Q: One of the two forces is double the other and their resultant is equal to the greater force . The angle between them is ? Ans : Its answer is cos^-1 (-1/4) My solution : The formula for Cosine law is R= √A²+B² +2ABcos theta Our teacher...

Homework Statement To avoid restricted airspace, a pilot on a VFR cross country flight plans the following 3 legs immediately after takeoff. Leg A (280 heading 40nm distance) Leg B (240 heading 30nm distance) Leg C (200 heading 25nm) What one heading and distance from takeoff would...

A ship sails 130 km due north from island A to island B and then 92 km, in the direction 22° south of east, to island C. The ship after that returns directly to island A. Calculate the magnitude and direction of the displacement vector in the last trip. Draw appropriate diagrams. Homework...

Two cars approaching each other with speed 100km/h each. Relative to one of the cars the road moves with the speed of 100km/h (car pulls it toward itself), the other car moves on the moving road, vectors add - relative velocity 200 km/h just the way it should be. Relative to the road two cars...

Homework Statement Find the magnitude and direction of the resultant force Fr=F1+F2+F3 by first finding F'=F1+F2 then Fr=F'+F3 known values are in the link Homework Equations Basic vector addition. Law of cosines. Law of sines. The Attempt at a Solution Here's my attempt. I'm not convinced by...

Homework Statement Hello, this is my first time taking physics in college, and I have read the section twice and I this is what I understand. If someone could point me in the right direction, that would be great. For example: How do I find the angle for example from Vector a + Vector b. Would...

There seems to be problem with the answer to this problem. Weirdly, they get that the x component of F1 is 3N! Then, when they end up calculating the direction in C, they get 9.5°. I get 9.16°. Am I the one going crazy? This is fairly straight-forward!

can we consider gravitational field, magnetic field and electrical field as vector? can see the net result of this field.

Homework Statement If vector A + vector B = vector C and magnitude A + magnitude B = magnitude C how are vector A and B relative to each other. Homework Equations The Attempt at a Solution I need help understanding this question. I know that in order for them to be equal they...

If the tangent space at p is a true vector space, then it must be that the sum of two vectors is itself a directional derivative operator along some path passing through p. I've been trying to prove that this is true without any luck. My textbook "proves" that vector addition is closed by...

Homework Statement A 20 kg object is being acted on by a 90 N [E60N] force, a 40 N [S] force, and a 40 N [E27S] force. Find the net force acting on the object and its acceleration. Homework Equations ƩF = ma The Attempt at a Solution I understand that I have to add vector...

Homework Statement Suppose a plane flies at a constant groundspeed of 500 miles per hour due east and encounters a 50 mile-per-hour wind from the northwest. Both the airspeed and the compass direction must change to for the plane to maintain its groundspeed and eastward direction. Find the...

I'm trying to do this homework problem but I keep getting an answer that is not given. Can someone tell me what I am doing wrong please. This is for University level calc 3. Homework Statement Homework Equations A vector U=<x,y> ||U|| means the length of U = √(x^2 +y^2). vectors can also...

Homework Statement http://grephysics.net/ans/0177/23 The answer to this problem is confusing me. So you can calculate the normal acceleration and tangential acceleration to each by equal and 90° apart from each other, so their final vector has an angel of 45°. However, if the speed travels...

I am stuck on this one: According to me, the only correct answers are \vec{r} = \vec{t} - \vec{s} \\ \vec{r} + \vec{s} = \vec{t} But according to the key, these are also correct \vec{r} + \vec{t} = \vec{s} \\ \vec{s} + \vec{t} = \vec{r} I honestly do not see how, can somebody...

Homework Statement Three vectors, A, B and C each have a magnitude of 50 units. Their directions relative to the positive direction of the x-axis are 20°, 160° and 270°, respectively. Calculate the magnitude and direction of each of the following vectors. 1.) A + B + C 2.) A-B+C 3.)...

Homework Statement Joe pushes on the handle of a 10 kg lawn spreader. The handle makes a 45° angle with the horizontal. Joe wishes to accelerate the spreader from rest to 1.39 m/s in 1.5s. What force must Joe apply to the handle? Neglect friction. Homework Equations A=Vf-Vi/t. F=ma...

Homework Statement Vectors a and b have magnitudes 2 and 3. The angle between them is 50 degrees. Determine 5a - 2b and determine its magnitude and direction Homework Equations Cosine Law and Sine Law The Attempt at a Solution I can solve for the magnitude using the cos law and...

I solved a word problem correctly...But I'm a little confused about what my answer means, I guess I'm having trouble understanding how they got the meaning of the numbers. My question is about step (b). Problem: The velocity of an aircraft is 200 km/hr due west. A northwest wind of 50 km/hr is...

If a neutron in a nucleus is in a 1p state, before splitting this up into separate j-state (due to spin-orbit effect) this neutron has 6 possible states. l = 1 m_l = 1, 0 or -1 m_s = 1/2 or -1/2Splitting this into j-states corresponding to l+s and l-s, as expected there are 6 states. j = 3/2...

Homework Statement Alright so i need to add these using vector addition i suppose. P = M + N P = 1.8304 kgxm/s (S 6° W) + 3.2864 kgxm/s (S 42° W) The Attempt at a Solution This is my half attempt: http://s1176.beta.photobucket.com/user/LolaGoesLala/media/ggfgf.jpg.html But i don't...

Homework Statement Given the following Vectors: A+B= x1i + y1j and A-B= x2i + y2j what is A? and what is B? The Attempt at a Solution I wasn't really sure how to go about this problem. I tried setting one side to A and pluging it into the other eqn A.. however that made no sense to me.

The triangle inequality states that, the sum of any two sides of a triangle must be greater than the third side of the triangle. But the triangle law of vector addition states that if we can represent two vectors as the two sides of a triangle in one order ,the third side of the triangle...

I have a puzzling question that a gentleman discussed and have differnt view on the problem, the probelm goes as follows: What is know is the Resultant of a Vector Addition, the goal is to find the two vectors from which the resultant came from. The other piece of information that is know is...

Homework Statement Homework Equations The Attempt at a Solution Do you see how 1 1 1 changes to 3 3 3. i know why gaussian elimination you can change any vector by multiplying it by anything you want. but for some reason i have difficulty believing that you're allowed to do that here. is...

I'm reading through a multivariable calculus book and it starts off with some linear algebra. It defines vector addition as V \times V \rightarrow V. My text describes V as a set and describes the above process as a mapping. I believe the \times may represent a Cartesian product. Could someone...

I'm not sure if this the correct area but Ill go ahead anyways. I have three points (A, B, and C) in 3D space that form a triangle. All three points have the (x,y,z) coordinates defined. Using the dot product I have solved for the angle θ (or in other notation the angle ABC) of the...

Mastering physics Knight. 2nd edition. A figure shows two dots of a motion diagram and vector \vec{V}_{1} Copy this figure and add vector \vec{V}_{2} and dot 3 if the accelration vector \vec{a} at dot 2 (a) points up and (b) points down. \vec{V}_{1} is a vertical vector pointing upward with...

Homework Statement Vectors A and B have equal magnitudes of 10.0. If the sum of A and B is the vector 3.13j , determine the angle between A and B Homework Equations none The Attempt at a Solution I gave both A and B the length r=10 I don't know how to add them together if I don't...

Homework Statement There are two forces on the 3.2 kg box in the overhead view of the figure below but only one is shown. The figure also shows the acceleration of the box. F1 is in Q I and F2 is in Q III a = 12m/s2 there is a picture here that I do not know how to upload -- it shows F1 in...

Homework Statement Two vectors are given by a = 2.3 x - 9.7 y and b = -18.6 x + 2.8 y. What is the magnitude of a? What is the angle between vector b and the positive x-axis? What is the magnitude of the vector a + b? Homework Equations I don't know The Attempt at a Solution...

This a book example that I have the answer to but do not understand. What are the magnitude and direction of the total displacement for the treasure hunt? The instructions to find the treasure are 5 paces North, 3 paces East, then 4 paces Southeast. Each pace is 0.750 m in length. So I...

Should be quite easy, really, given that it's just adding things together, hey ho. Problem a position vector of point (1), identified by sherical coordinates, is 5m away from point (2). I have a unit vector R1,2 identified by spherical coordinates [Aex - Bey +Cez], giving the direction to...

This seems to be a very perplexing problem to which there is much difficulty of making sense of. So instead of trying to rewrite the problem in pieces, I've decided to provide the entire image leading up to the question so that you are seeing what I'm seeing. Hopefully, if I can describe where...

Homework Statement Find y component of vector C from its length and the angle it makes with the x axis, that is, from geometry. Express the y component of vector C in terms of C and \phi. Homework Equations Vector addition using geometry: 1) C = \sqrt{A^{2}+B^{2}-2ABcos(c)}...

Homework Statement Find the resultant for the following directions. 20 degrees east of south for 1/2" 80 degrees South of west for 5" 15 degrees west of north for 1" 35 degrees North of East for 3" 40 degrees South of East for 1"Homework Equations R2 = a2 + b2 The Attempt at a Solution i...

Homework Statement A = 2i + 3j B = -5i + 6j Calculate (draw vector diagram) A + B A - B Homework Equations actually we're just confused as to whether we need to use the angles to answer this or just answer it directly, meaning that for A + B the answer would be -3i + 9j The...

I am having a lot of trouble with my homework. If anyone could help me, it would be much appreciated. The Smith's go on vacation. They travel 16.0 km north/west; then turn 27 degrees to the left and go 135 km; then 294 km south/west. What is their displacement from home? So I found the X...

Homework Statement 1) A boy is floating on a raft in a river. THe water flows at a speed of 12m/s east. The boy's feet kick the water,causing a velocity of 2m/s at an angle of 43 degrees north of east. Using Vector components, calculate the magnitude of the raft's velocity. 2)One vector...

Homework Statement A plane heads 20° north of east at 200 m/s. The wind blows 60° north of east at 50 m/s. What is the resultant velocity of the plane? Homework Equations Δv= v2-v1 or Δv= v2+(-v1) The Attempt at a Solution I know you have to solve for the x and y, but I don't know...

Homework Statement 1) Two men are near a hole, One man walks 12m east and then 12m North from a hole, the other walks 15m west and then 11m north, Find the dot product of their net displacements from the tree _______ 2) Vector A = -i +2j - 5k, Vector B = 3i +2j -2k Find the magnitude...

Homework Statement [PLAIN]http://img6.imageshack.us/img6/4057/pictureforforums.png A hiker walks 8.33 km 30 degrees N of E then 4.97 km 45 degrees N of W and finally 7.32 km 60 degrees S of E. How far and in what direction is the hiker from the original position (A) to (B) Homework...

Homework Statement [PLAIN]http://img849.imageshack.us/img849/1466/vectorimage.png Homework Equations The Attempt at a Solution I'm not sure at all how to do this to get the resultant vector, other than using the head-to-tail method by scaled vectors, which I really don't want...

Hello Everyone, I was just wondering if there was a way to add two vectors that are determined by spherical coordinates (radius, theta, phi). For example, if I have v1 = (5, Pi/4, Pi/2) and v2 = (3, Pi, -Pi/2) is there a way to add these using their respective radii, thetas, and phis or do I...