Question

Find a unit vector in the direction of \( \overrightarrow a = 3\hat i - 2\hat j + 6\hat k \)

Answer 1

Answer:

a / |a| = (3/7) i  -  (2/7) j  +  (6/7) k

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Step-by-step explanation:

Just take the vector

a / |a|

By dividing by |a|, you'll be left with a vector of magnitude 1; i.e. a unit vector.

Just need

|a|² = 3² + (-2)² + 6² = 9 + 4 + 36 = 49  =>  |a| = 7

So the vector we want is

a / |a| = (3/7) i  -  (2/7) j  +  (6/7) k