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)

the journeys of marquette, joliet and la salle a) new france expand.

all three of these explorers explored the midwest and the area around the great lakes, which they subsequently claimed for france.

this was a big portion of territory and expanded new france which before then only consisted of quebec province in northeastern canada