Question

Area of a rectangle having vertices $A,B,C$ and $D$ with position vectors $-\hat{i}+\frac{1}{2}\hat{j}+4\hat{k}$,$\hat{i}+\frac{1}{2}\hat{j}+4\hat{k}$,$\hat{i}-\frac{1}{2}\hat{j}+4\hat{k}$ and $-\hat{i}-\frac{1}{2}\hat{j}+4\hat{k}$

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

Answer 1

The correct option is C $2$

$|AB|=\sqrt{(1-1{)}^2+{(\frac{1}{2}-\frac{1}{2})}^2+(4-4{)}^2}$

$=2$

$|BC|=\sqrt{(1-1{)}^2+{(\frac{1}{2}+\frac{1}{2})}^2+(4-4{)}^2}=1$

Area $=|AB|\times |BC|$

$=2$