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

• $\cfrac{1}{2}$

• $1$

• $2$

• $4$

{Correct Option is c}

Here, $\overrightarrow {AB} = (\hat i + \cfrac{1}{2}\hat j + 4\hat k) - ( - \hat i + \cfrac{1}{2}\hat j + 4\hat k) = 2\hat i$
$\Rightarrow |\overrightarrow {AB} | = 2$

and $\overrightarrow {AD} = ( - \hat i - \cfrac{1}{2}\hat j + 4\hat k) - ( - \hat i + \cfrac{1}{2}\hat j + 4\hat k) = - \hat j$

$\Rightarrow |\overrightarrow {AD} | = 1$
$\Rightarrow$ Area of rectangle

Miscellaneous Exercise