JEE Main & Advanced Physics Vectors Question Bank Topic Test - Vectors

The three vectors \[\vec{A}=3\hat{i}-2\hat{j}-\hat{k},\]\[\vec{B}=\hat{i}-3\hat{j}+5\hat{k}\] and \[\vec{C}=2\hat{i}-\hat{j}-4\hat{k}\] does not form

A) an equilateral triangle

B) isosceles triangle

C) a right angled triangle

D) no triangle

Correct Answer: A

Solution :

[a]

\[\vec{A}=3\hat{i}-2\hat{j}+\hat{k},\,\vec{B}=\hat{i}-3\hat{j}+5\hat{k},\,\vec{C}=2\hat{i}-\hat{j}+4\hat{k}\]

\[|\vec{A}|=\sqrt{{{3}^{2}}+{{(-2)}^{2}}+{{1}^{2}}}=\sqrt{9+4+1}=\sqrt{14}\]

\[|\vec{B}|=\sqrt{{{1}^{2}}+{{(-3)}^{2}}+{{5}^{2}}}=\sqrt{1+9+25}=\sqrt{35}\]

\[|\vec{C}|=\sqrt{{{2}^{2}}+{{1}^{2}}+{{(-4)}^{2}}}=\sqrt{4+1+16}=\sqrt{21}\]

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