Browse Questions

# The vector having initial and terminal points as $(2,5,0)$ and $(-3,7,4)$ respectively is

$\begin{array}{1 1}(A)\;\hat i+12\hat j+4\hat k & (B)\;5\hat i+2\hat j+4\hat k\\(C)\;-5\hat i+2\hat j+4\hat k & (D)\;\hat i-\hat j+\hat k\end{array}$

Toolbox:
• The vector joining of the terminal point B to the initial point A given by $\overrightarrow {AB}=\overrightarrow {OB}-\overrightarrow{OA}$
Let $\overrightarrow {OA}=2 \hat i+5 \hat j+0 \hat k$ and $\overrightarrow {OB}=-3\hat i+7 \hat j+4 \hat k$
Therefore $\overrightarrow {AB}=\overrightarrow {OB}-\overrightarrow {OA}$
Now substitutie for $\overrightarrow {OA}$ and $\overrightarrow {OB}$
$=(-3\hat i+7 \hat j+4 \hat k)-(2 \hat i+5 \hat j+0 \hat k)$
On simplifying we get,
$=- 5\hat i + 2\hat j + 4\hat k$
Hence the correct option is $C$