What is the angle between vectors A and B?

In summary, ehild was doing some calculations wrong and then found out that she needed to use inverse cosine instead of sine to solve the problem.
  • #1
MozAngeles
101
0

Homework Statement



Two vectors A and B have magnitude A = 2.99 and B = 3.10. Their vector product is A X B = -4.98 k + 2.08 i . What is the angle between A and B?

Homework Equations


C= ABsinθ
C=A X B


The Attempt at a Solution


θ= arcsin C/(⎮A⎮⎮B⎮)
so i found the magnitude for C, then divided by (a times b), then took the sin inverse. Where i got theta = 53 degrees but this was wrong. Can someone please point me in the right direciton?
 
Physics news on Phys.org
  • #2
Suppose you have the three vectors A=i, B=i+j, and C=-i+j. Then |A|=1 and |B|=|C|=sqrt(2). You also have AxB = k and AxC = k, so sin(A,B) = sin(A,C) = 1/sqrt(2).

Sketch the vectors in the xy-plane and you'll see what's going on. The same thing is happening in your problem.
 
  • #3
Hi, I'm sorry i sketched it out and it still does not make sense... I'm really still quite lost...
 
  • #4
What's the angle between A and B and between A and C? (from the sketch)
 
  • #5
MozAngeles said:

The Attempt at a Solution


θ= arcsin C/(⎮A⎮⎮B⎮)
so i found the magnitude for C, then divided by (a times b), then took the sin inverse. Where i got theta = 53 degrees but this was wrong.

You miscalculated something. Are you sure you did not use inverse cosine instead of sine? Show your work in detail.

ehild
 
  • #6
Oops, I guess I should have solved the problem myself. :redface:

Never mind what I said above. Listen to ehild.
 
  • #7
Vela,

Is it possible and how to find out from these data if the angle enclosed by the vectors A and B is less than or greater than 90°? I do not see it now.

ehild
 
  • #8
You can't, just from the lengths. The length of \(\displaystyle A\times B\) is the same as the length of \(\displaystyle A\times (-B)\). If the angle between A and B is less than 90 degrees then the angle between A and -B is larger than 90 degrees.
 
  • #9
No, you can't, not without more info.
 
  • #10
Thanks.

ehild
 
  • #11
I was doing it right initially, my calculations were wrong. Thanks for your help anyways!
 

FAQ: What is the angle between vectors A and B?

What is a vector?

A vector is a mathematical object that represents both magnitude (size or length) and direction. It is typically represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction of the vector.

How are vectors and angles related?

Vectors and angles are related because the direction of a vector is described by the angle it makes with a reference direction. This angle is typically measured in degrees or radians.

What is the cross product of two vectors?

The cross product of two vectors is a vector that is perpendicular to both of the original vectors. It is calculated by multiplying the magnitudes of the two vectors, the sine of the angle between them, and a unit vector in the direction of the perpendicular vector.

How is the cross product used in physics and engineering?

The cross product is used in physics and engineering to calculate the torque or moment of a force, to determine the direction of a magnetic field, and to find the normal vector to a plane. It is also used in 3D graphics to calculate lighting and shading effects.

Can you give an example of a real-life application of vectors, angles, and the cross product?

One example of a real-life application is in the design of bridges and buildings. Engineers use vectors and the cross product to calculate the forces and moments acting on different parts of the structure, and to ensure that the structure can withstand these forces without collapsing.

Similar threads

Torque on a Circular Current Loop under a Misaligned Magnetic Field
Replies
1
Views
498
Vector cross product anti-commutative property
Replies
9
Views
2K
What Is the Correct Angle Between Two Vectors If Their Cross Product Is Known?
Replies
1
Views
1K
The derivative of the dot product "distributes" over each vector
Replies
5
Views
243
Finding dot product, cross, and angle between 2 vectors
Replies
3
Views
1K
Vectors in yz and xz plane dot product, cross product, and angle
Replies
8
Views
1K
Finding the magnitude (length) and direction (angle) of a vector
Replies
2
Views
991
What is the sine of the angle between two given vectors?
Replies
6
Views
2K
B Confusion about the angle between two vectors in a cross product
Replies
7
Views
2K
Finding the Angle Between Vectors A and B in the Cross Product
Replies
13
Views
2K

Hot Threads

Recent Insights

Back
Top