# 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)

###### 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?