Question

Find a vector that has the same direction as −2, 4, 6 but has length 6.

Answer 1

We are givem vector < −2, 4, 6 >

First we would find norm of given vector.

In order words norm is the length of given vector.

Length of given vector ||v|| = || −2, 4, 6 || = $\sqrt{(-2)^2+(4)^2+(6)^2}$

||v|| = $\sqrt{4+16+36}$

$=\sqrt{56}=2\sqrt{14}$

Now, we need to find a vector in the same direction as given vector but length is 6.

So, dividing 6 by the length of given vector.

We get $\frac{6}{2\sqrt{14}}=\frac{3}{\sqrt{14}}$

Multiplying this value by given vector, we get

$\frac{3}{\sqrt{14}}<-2, 4, 6> = <\frac{-6}{\sqrt{14}},\frac{12}{\sqrt{14}},\frac{18}{\sqrt{14}}>$