Question

The vector $w$ with intial point $(a,b,c)$ and final point $(a+1,b+2,c+3)$ is :

• A. $(a,2,c+3)$
• B. $(a,b+2,c+3)$
• C. $(a-1,b-2,c-3)$
• D. $(1,2,3)$

Answer 1

The correct option is D $(1,2,3)$

Given points :
$A(a,b,c)$ and $B(a+1,b+2,c+3)$
$\overrightarrow{OA}=a\hat{i}+b\hat{j}+c\hat{k}$
$\overrightarrow{OB}=(a+1)\hat{i}+(b+2)\hat{j}+(c+3)\hat{k}$
Vector $w$ from $A$ to $B$ is
$\overrightarrow{AB}=\overrightarrow{OB}-\overrightarrow{OA}$
$\overrightarrow{AB}=\hat{i}+2\hat{j}+3\hat{k}=(1,2,3)$