Question

Let $A=2\overline{i}+4\overline{k}$, $B=5\overline{i}+3\sqrt{3}\overline{j}+4\overline{k},C=-2\sqrt{3}\overline{j}+\overline{k}$, $D=2\overline{i}+\overline{k}$ then the value of $CD$ in terms of$AB$ is

• A. $AB$
• B. $\frac{1}{3}AB$
• C. $\frac{2}{3}AB$
• D. $\frac{1}{4}AB$

Answer 1

The correct option is C $\frac{2}{3}AB$

$\overrightarrow{CD}=2\hat{i}+\hat{k}-(-2\sqrt{3}\hat{j}+\hat{k})$
$\overrightarrow{CD}=2\hat{i}+2\sqrt{3}\hat{j}$ ________(1)
$\overrightarrow{AB}=(5\hat{i}+3\sqrt{3}\hat{j}+4\hat{k})-(2\hat{i}+4\hat{k})$
$\overrightarrow{AB}=3\hat{i}+3\sqrt{3}\hat{j}$ _________(2)
$\frac{2}{3}\overrightarrow{AB}=\overrightarrow{CD}$