Question

Find the vector $w$ with the initial point $(4,1,2)$ and final point $(1,6,5)$.

• A. $(3,-5,-3)$
• B. $(0,7,3)$
• C. $(-3,5,3)$
• D. None of these

Answer 1

The correct option is C $(-3,5,3)$

Given points

$A(4,1,2)$ and $B(1,6,5)$

$\overrightarrow{OA}=4\hat{i}+\hat{j}+2\hat{k}$

$\overrightarrow{OB}=\hat{i}+6\hat{j}+5\hat{k}$

vector

$\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}$

$\overrightarrow{AB}=\hat{i}+6\hat{j}+5\hat{k}-(4\hat{i}+\hat{j}+2\hat{k})$

$\overrightarrow{AB}=\hat{i}+6\hat{j}+5\hat{k}-4\hat{i}-\hat{j}-2\hat{k}$

$\overrightarrow{AB}=-3\hat{i}+5\hat{j}+3\hat{k}$

$AB=(-3,5,3)$