Consider the vector below. Determine its length and direction. Vector: 2i+11j+5k2i+11j+5k Magnitude: Direction (unitized):
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Ответ:
Magnitude:
, Direction (unitized): ![\vec u = \frac{\sqrt{6}}{6}\,\hat{i} + \frac{11\sqrt{6}}{12}\,\hat{j}+\frac{5\sqrt{6}}{12}\,\hat{k}](/tpl/images/0977/8515/409b5.png)
Explanation:
Let
. The magnitude of the vector is represented by the Pythagorean formula:
And the direction is represented by the direction cosines, measured in sexagesimal degrees, that is:
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:
Ответ:
The answer to your question is D