Question

Area is a vector quantity. How?

Answer 1

$Areaofatriangleusingvector;$

$\Delta =\frac{1}{2}\left(base\right)\left(height\right)$

$\Delta =\frac{1}{2}ABsin\theta$

$\Delta =\frac{ABsin\theta }{2}=\frac{|\overrightarrow{A}\times \overrightarrow{B}|}{2}$

Note: we can also define any surface's area as a vector quantity depends on the requirement. simply define an area as a vector using unit vector tool, i.e.

$\hat{a}=\frac{\overrightarrow{A}}{\left|A\right|}$

$\overrightarrow{A}=\left|A\right|\hat{a};where\left|A\right|=magnitudeoftheareaand\hat{a}=directionofunitvector.$