Consider the vector below. Determine its length and direction. Vector: 2i+11j+5k2i+11j+5k Magnitude: Direction (unitized):

Magnitude: , Direction (unitized):

Explanation:

Let . The magnitude of the vector is represented by the Pythagorean formula:

(1)

And the direction is represented by the direction cosines, measured in sexagesimal degrees, that is:

(2)

(3)

(4)

If we know that , and , then the magnitude and directions of the vector are, respectively:

The direction can be represented by the following unit vector:

(5)

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