Q 45.

Find a vector in the direction of $<8, - 7, 2>$ and with magnitude 2.

Verified

Answer

The required vector is $\frac{2}{\sqrt{117}} <8, - 7, 2>$ .

1Step 1. Given information.

The given vector is:

$v = <8, - 7, 2>$ with magnitude 2.

2Step 2. Find the norm of the vector.

$v = <8, - 7, 2> ||v|| = \sqrt{8^{2} + {(- 7)}^{2} + 2^{2}} = \sqrt{64 + 49 + 4} = \sqrt{117}$

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:

$\frac{a}{||v||} v = \frac{2}{\sqrt{117}} <8, - 7, 2>$

Therefore the vector in the direction of $v = <8, - 7, 2>$ and with a magnitude of 2 is $\frac{2}{\sqrt{117}} <8, - 7, 2>$ .