Question

The three vectors $\overset{\rightarrow}{A} = 3\widehat{i} - 2\widehat{j} + \widehat{k},\overset{\rightarrow}{B} = \widehat{i} - 3\widehat{j} + 5\widehat{k}$ and

$\overset{\rightarrow}{C} = 2\widehat{i} + \widehat{j} - 4\widehat{k}$ form

• A. An equilateral triangle
• B. Isosceles triangle
• C. A right angled triangle
• D. No triangle

Answer 1

Answer: (C)

A right angled triangle

Answer 2

$\overrightarrow{A} = 3\widehat{i} - 2\widehat{j} + \widehat{k}$, $\overrightarrow{B} = \widehat{i} - 3\widehat{j} + 5\widehat{k}$, $\overrightarrow{C} = 2\widehat{i} - \widehat{j} + 4\widehat{k}$

$|\overrightarrow{A}| = \sqrt{3^{2} + ( - 2)^{2} + 1^{2}} = \sqrt{9 + 4 + 1} = \sqrt{14}$

$|\overrightarrow{B}| = \sqrt{1^{2} + ( - 3)^{2} + 5^{2}} = \sqrt{1 + 9 + 25} = \sqrt{35}$

$|\overrightarrow{A}| = \sqrt{2^{2} + 1^{2} + ( - 4)^{2}} = \sqrt{4 + 1 + 16} = \sqrt{21}$

As $B = \sqrt{A^{2} + C^{2}}$therefore ABC will be right angled triangle.