Physics Practice Problems Unit Vectors Practice Problems Solution: Let V = 20.5 i + 22.5 j − 13.5 k.(a) Find the magn...

Solution: 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?

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?

Solution

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

A=Ax i^+Ay j^+Az k^

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:

|A|=Ax2+Ay2+Az2 (1)

Ax=|A| cos α (2)

Ay=|A| cos β   (3)

Az=|A| cos γ   (4)

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