Question

$\overrightarrow{AB}\times \overrightarrow{AC}=2\hat{i}-4\hat{j}+4\hat{k}$ then the area of triangle $ABC$ is

• A. $3squnits$
• B. $4squnits$
• C. $16squnits$
• D. $9squnits$

Answer 1

The correct option is A

$3squnits$

Explanation for the correct option:

Step- 1: Find the magnitude of the given cross product:

We have been given a cross product of sides of the triangle, $\overrightarrow{AB}\times \overrightarrow{AC}=2\hat{i}-4\hat{j}+4\hat{k}$

We need to find the area of the triangle $ABC$

The magnitude $\overrightarrow{AB}\times \overrightarrow{AC}$ would be,

$$\begin{gathered} =|\overrightarrow{AB}\times \overrightarrow{AC}| \\ =\sqrt{2^2+{(-4)}^2+4^2} \\ =\sqrt{4+16+16} \\ =\sqrt{36} \\ =6 \end{gathered}$$

Step- 2: Find the area of the triangle $\mathbf{ABC}$:

The area of the triangle $ABC$ would be,

$$\begin{gathered} =\frac{1}{2}\times |\overrightarrow{AB}\times \overrightarrow{AC}| \\ =\frac{1}{2}\times 6 \\ =3squnits. \end{gathered}$$

Therefore, option (A) is the correct option.