Q 40.

In Exercises 37–42, find $||v||$ and find the unit vector in the direction of v.

$v = <2, 1, - 5>$

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Answer

$||v|| = \sqrt{30}$ and the unit vector in the direction of v is $\frac{1}{\sqrt{30}} <2, 1, - 5>$ .

1Step 1. Given information.

The given vector is:

$v = <2, 1, - 5>$

2Step 2. Find the norm of the vector.

$v = <2, 1, - 5> ||v|| = \sqrt{2^{2} + 1^{2} + {(5)}^{2}} = \sqrt{4 + 1 + 25} = \sqrt{30}$

Therefore, the norm of the given vector is $\sqrt{30}$ .

3Step 3. Find the unit vector in the direction of v .

The unit vector in the direction of v is the vector:

$\frac{1}{||v||} v = \frac{1}{\sqrt{30}} <2, 1, - 5>$

Therefore, the unit vector in the direction of $v = <2, 1, - 5>$ is $\frac{1}{\sqrt{30}} <2, 1, - 5>$ .