Q 46.

Find a vector in the direction of $<9, 0, - 6>$ and with magnitude 7.

Verified

Answer

The required vector is $\frac{7}{\sqrt{117}} <9, 0, - 6>$ .

1Step 1. Given information.

The given vector is:

$v = <9, 0, - 6>$ with magnitude 7.

2Step 2. Find the norm of the vector.

$v = <9, 0, - 6> ||v|| = \sqrt{9^{2} + 0^{2} + {(- 6)}^{2}} = \sqrt{81 + 0 + 36} = \sqrt{117}$

Therefore, the norm of the given vector is $\sqrt{117}$ .

3Step 3. Find the vector.

We know that the vector in the direction of v is $\frac{a}{||v||} v$ . Here a is the magnitude of the given vector.

The required vector is:

$\frac{a}{||v||} v = \frac{7}{\sqrt{117}} <9, 0, - 6>$

Therefore the vector in the direction of $v = <9, 0, - 6>$ and with a magnitude of 7 is $\frac{7}{\sqrt{117}} <9, 0, - 6>$ .