Question

The vectors $2\overrightarrow{i}+3\overrightarrow{j}+4\overrightarrow{k},3\overrightarrow{i}+2\overrightarrow{j}-3\overrightarrow{k}$, and $5\overrightarrow{i}+5\overrightarrow{j}+\overrightarrow{k}$ form:

• A. an equilateral triangle
• B. an isosceles triangle
• C. right angled triangle
• D. circle

Answer 1

The correct option is C right angled triangle

$\overrightarrow{a}=2\overrightarrow{i}+3\overrightarrow{j}+4\overrightarrow{k}\overrightarrow{b}=3\overrightarrow{i}+2\overrightarrow{j}-3\overrightarrow{k}\overrightarrow{c}=5\overrightarrow{i}+5\overrightarrow{j}+1\overrightarrow{k}\Rightarrow \overrightarrow{c}=\overrightarrow{a}+\overrightarrow{b}$

Hence, $\overrightarrow{c},\overrightarrow{a}and\overrightarrow{b}$ form a triangle.

Let, angle between

$\overrightarrow{a}and\overrightarrow{b}=\theta \Rightarrow \cos \theta =\frac{\overrightarrow{a}\cdot \overrightarrow{b}}{\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|}=0\Rightarrow \theta =\frac{\pi }{2}$