Question

The vector which joins the point $A(4,5,6)$ to $B(10,11,12)$ is

• A. $2\hat{i}+2\hat{j}+2\hat{k}$
• B. $4\hat{i}+4\hat{j}+4\hat{k}$
• C. $6\hat{i}+6\hat{j}+6\hat{k}$
• D. $8\hat{i}+8\hat{j}+8\hat{k}$

Answer 1

The correct option is C $6\hat{i}+6\hat{j}+6\hat{k}$

Given points, $A(4,5,6)$ to $B(10,11,12)$
$\Rightarrow \overrightarrow{OA}=4\hat{i}+5\hat{j}+6\hat{k}\Rightarrow \overrightarrow{OB}=10\hat{i}+11\hat{j}+12\hat{k}$
So, $\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}=10\hat{i}+11\hat{j}+12\hat{k}-(4\hat{i}+5\hat{j}+6\hat{k})=6\hat{i}+6\hat{j}+6\hat{k}$