Question

The vector $3\hat{i}+5\hat{j}+2\hat{k},2\hat{i}-3\hat{j}-5\hat{k}$ and $5\hat{i}+2\hat{j}-3\hat{k}$ form the sides of a/an

• A. Right angled triangle
• B. Isoscales triangle
• C. Equilateral triangle
• D. None of these

Answer 1

Answer: (C)

Equilateral triangle

Let the given vectors be

$\begin{array}{c}\overrightarrow{A}=3\hat{i}+5\hat{j}+2\hat{k}\\ \overrightarrow{B}=2\hat{i}-3\hat{j}-5\hat{k}\\ \overrightarrow{C}=5\hat{i}+2\hat{j}-3\hat{k}\\ |\overrightarrow{A}|=\sqrt{{\left(3\right)}^2+{\left(5\right)}^2+{\left(2\right)}^2}=\sqrt{38}\\ |\overrightarrow{B}|=\sqrt{{\left(2\right)}^2+{\left(-3\right)}^2+{\left(-5\right)}^2}=\sqrt{38}\\ |\overrightarrow{C}|=\sqrt{{\left(5\right)}^2+{\left(2\right)}^2+{\left(-3\right)}^2}=\sqrt{38}\end{array}$

since $|\overrightarrow{A}|=|\overrightarrow{B}|=|\overrightarrow{C}|$

So, The given vectors form the sides of an equilateral triangle.