Question

The perimeter of a triangle with sides $3\hat{i}+4\hat{j}+5\hat{k},4\hat{i}-3\hat{j}-5\hat{k}$ and $7\hat{i}+\hat{j}$ is

• A. $\sqrt{450}$
• B. $\sqrt{150}$
• C. $\sqrt{50}$
• D. $\sqrt{200}$

Answer 1

The correct option is A $\sqrt{450}$

Let,

$\begin{array}{c}A=\left(0,0,0\right)\\ \overrightarrow{AB}=3\hat{i}+4\hat{j}+5\hat{k}\\ \overrightarrow{B}=\left(3,4,5\right)\\ \overrightarrow{AC}=7\hat{i}+\hat{j}\\ \overrightarrow{C}=\left(7,1,0\right)\\ AB=\sqrt{9+16+25}=\sqrt{50}\\ BC=\sqrt{16+9++25}=\sqrt{50}\\ CA=\sqrt{50}\end{array}$

Perimeter:-

$\begin{array}{c}=3\sqrt{50}\\ =\sqrt{450}\end{array}$

Then,

Option $A$ is correct answer.