Question

Find the unit vector in the direction opposite to the direction of the vector $6\hat{i}-8\hat{j}+10\hat{k}$

• A. $-6\hat{i}+8\hat{j}-10\hat{k}$
• B. $\left(\frac{-6}{10}\right)\hat{i}+\left(\frac{8}{10}\right)\hat{j}-\left(\frac{10}{10}\right)\hat{k}$
• C. $\left(\frac{-6}{\sqrt{200}}\right)\hat{i}+\left(\frac{8}{\sqrt{200}}\right)\hat{j}-\left(\frac{10}{\sqrt{200}}\right)\hat{k}$
• D. None of these.

Answer 1

The correct option is C

$\left(\frac{-6}{\sqrt{200}}\right)\hat{i}+\left(\frac{8}{\sqrt{200}}\right)\hat{j}-\left(\frac{10}{\sqrt{200}}\right)\hat{k}$

Given vector = $6\hat{i}-8\hat{j}+10\hat{k}$

Opposite of this is $-6\hat{i}+8\hat{j}-10\hat{k}$

Now we need to find the unit vector in the given direction.

So we need to make sure that the magnitude of the vector so formed should be 1 units.

$\sqrt{(-6{)}^2+8^2+(-10{)}^2}=\sqrt{200}$

So if i divide the given vector by $\sqrt{200}$ i get a vector whose magnitude is 1 or in other words a unit vector.

So, $\left(\frac{-6}{\sqrt{200}}\right)\hat{i}+\left(\frac{8}{\sqrt{200}}\right)\hat{j}-\left(\frac{10}{\sqrt{200}}\right)\hat{k}$ is your correct option.