Q 43.

Find a vector in the direction of $<3, 1, 2>$ and with magnitude 5.

Verified

Answer

The required vector is $\frac{5}{\sqrt{14}} <3, 1, 2>$ .

1Step 1. Given information.

The given vector is:

$v = <3, 1, 2>$ with magnitude 5.

2Step 2. Find the norm of the vector.

$v = <3, 1, 2> ||v|| = \sqrt{3^{2} + 1^{2} + 2^{2}} = \sqrt{9 + 1 + 4} = \sqrt{14}$

Therefore, the norm of the given vector is $\sqrt{14}$ .

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:

$\frac{a}{||v||} v = \frac{5}{\sqrt{14}} <3, 1, 2>$

Therefore the vector in the direction of $v = <3, 1, 2>$ and with a magnitude of 5 is $\frac{5}{\sqrt{14}} <3, 1, 2>$ .