Question

If co-ordinates of a point P is (1, 2, 2) then unit vector along the position vector of the point P will be

• A. $\frac{1}{3}(\hat{i}+2\hat{j}+2\hat{k})$
• B. $\hat{i}+2\hat{j}+2\hat{k}$
• C. $\frac{1}{3}(\hat{i}-2\hat{j}-2\hat{k})$
• D. $\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}+\hat{k})$

Answer 1

The correct option is A $\frac{1}{3}(\hat{i}+2\hat{j}+2\hat{k})$

The position vector of point P will be the vector joining origin to P:

$\underset{OP}{\to }=(1-0)\hat{i}+(2-0)\hat{i}+(2-0)\hat{K}$ ( cordinates of P - (1,2,2))

$\underset{OP}{\to }=\hat{i}+2\hat{j}+2\hat{K}$

Unit Vector of any given vector is given by : $\hat{n}=\frac{\underset{OP}{\to }}{\left|\underset{OP}{\to }\right|}$

$\Rightarrow \hat{n}=\frac{\hat{i}+2\hat{j}+2\hat{k}}{\sqrt{1+4+4}}=\frac{1}{\sqrt{9}}(\hat{i}+2\hat{j}+2\hat{k})=\frac{\hat{i}}{3}+\frac{2\hat{j}}{3}+\frac{2\hat{k}}{3}$