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# Problem: Let V = 20.5 i + 22.5 j − 13.5 k.(a) Find the magnitude of V.(b) What angle does this vector make with the x-, y-, and z-axes?

###### FREE Expert Solution

Remember that the unit-vector form is a vector equation that relates a vector to its x, y, and components:

Anytime we're asked to relate the magnitude and direction of a three-dimensional vector to its components, there are four basic equations we might use:

$\overline{)\mathbf{|}\stackrel{\mathbf{⇀}}{\mathbit{A}}\mathbf{|}{\mathbf{=}}\sqrt{{{\mathbit{A}}_{\mathbit{x}}}^{\mathbf{2}}\mathbf{+}{{\mathbit{A}}_{\mathbit{y}}}^{\mathbf{2}}\mathbf{+}{{\mathbit{A}}_{\mathbit{z}}}^{\mathbf{2}}}}$ (1)

(2)

(3)

(4)

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###### Problem Details

Let V = 20.5 i + 22.5 j − 13.5 k.

(a) Find the magnitude of V.

(b) What angle does this vector make with the x-, y-, and z-axes?

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Unit Vectors concept. You can view video lessons to learn Unit Vectors. Or if you need more Unit Vectors practice, you can also practice Unit Vectors practice problems.