Calculate the Resultant Vector of 3D Vectors

In summary, to find the resultant vector of the given three dimensional vectors, you first add their components to get the resultant vector. Then, to find its magnitude, you can use the Pythagorean theorem twice, once for the xy plane vectors and once for the z-vector and the xy plane vector. The magnitude is equal to the square root of the sum of the squares of the resultant vector's components.
  • #1
chemguy990
5
0

Homework Statement



I am having a tough time finding the resultant vector of the the following three dimensional vector:

d1x=2.33 cm, d1y= 3.84 cm, d1z= -1.2cm
d2x=3.41 cm, d2y= -1.01 cm, d2z = -3.29 cm
d3x= -1.04 cm, d3y= 1.93 cm, d3z = 0 cm

Find the resultant vector magnitude.

Homework Equations





The Attempt at a Solution



I have added the vector components and got the following:
rx= 4.7, ry= 4.76, rz= -4.49

Not sure where to go next.
 
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  • #2
So you have calculated the sum of the three vectors (the resultant vector). Now how do you get its magnitude?
 
  • #3
I know using the pythagorean theorem will get the resultant for xy plane vectors...not sure how to get the third plane calculations.
 
  • #4
chemguy990 said:
I know using the pythagorean theorem will get the resultant for xy plane vectors...not sure how to get the third plane calculations.

You'd apply pythagorean a second time, using the z-vector and the xy plane vector... draw a picture if you are unsure...

so the magnitude of the resultant is just [tex]\sqrt{r_x^2 +r_y^2 + r_z^2}[/tex]
 

FAQ: Calculate the Resultant Vector of 3D Vectors

What is a resultant vector?

A resultant vector is a single vector that represents the sum of two or more vectors. It is the combination of magnitude and direction of the individual vectors.

How do you calculate the resultant vector of 3D vectors?

To calculate the resultant vector of 3D vectors, you need to first determine the x, y, and z components of each vector. Then, add the x, y, and z components separately to get the resultant vector's x, y, and z components. Finally, use the Pythagorean theorem to find the magnitude of the resultant vector and inverse trigonometric functions to find its direction.

Can the resultant vector be negative?

Yes, the resultant vector can be negative. This occurs when the individual vectors have opposite directions and cancel each other out, resulting in a negative magnitude for the resultant vector.

What is the difference between a scalar and a vector?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. Scalars are represented by a single number, while vectors are represented by an arrow with length and direction.

How do you represent a vector in 3D space?

A vector in 3D space can be represented by a directed line segment with an arrow pointing in the direction of the vector. The length of the line segment represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

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