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Computing the angles of Vector to x,y,z axisses

1. Homework Statement

A vector is given by R = 2.00 i + 1.70 j + 2.81 k.

(a) Find the magnitudes of the x, y, and z components.
x = 2
y = 1.70
z = 2.81
(b) Find the magnitude of R.
3.85
(c) Find the angle between R and the x axis.
?
Find the angle between R and the y axis.
?
Find the angle between R and the z axis.
?

3. The Attempt at a Solution
I have the correct answers for part (a)& (b) but very confused on (c) what I needed to do to find angle
 

Answers and Replies

43
0
You'll need to use the dot product. For two vectors a and b, the dot product is:

[itex]\vec{a}\cdot\vec{b} = a_xb_x + a_yb_y + a_zb_z = |a||b|cosθ[/itex]

You want to solve this for θ. What two vectors do you need to use to find the angle between R and the x-axis?

Edit: Just to be clear, in the above equation, θ is the angle between a and b. You already know that you have to use R, but what other vector can you use that points along the x-axis? The y-axis? The z-axis?
 
Last edited:
157
0
You are looking for the angle the displacement vector is from each axis. So for the angle from the x-axis you need to consider the displacement from the j and k components (similar to what you did in part b) and determine the corresponding angle to the triangle formed by the j/k displacement and the given i value.
 

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