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

Two forces \[{{\vec{F}}_{1}}=10\hat{i}-\hat{j}-15\hat{k}\] and \[{{\vec{F}}_{2}}=10\hat{i}-\hat{j}-15\hat{k}\] act on a single point. The angle between \[{{\vec{F}}_{1}}\] and \[{{\vec{F}}_{2}}\] is nearly

A) \[{{30}^{o}}\]

B) \[{{45}^{o}}\]

C) \[{{60}^{o}}\]

D) \[{{90}^{o}}\]

Correct Answer: B

Solution :

[b] \[\cos \theta =\frac{{{{\vec{F}}}_{1}}.{{{\vec{F}}}_{2}}}{|{{{\vec{F}}}_{1}}|\,|{{{\vec{F}}}_{2}}|}\]

\[=\frac{(5\hat{i}+10\hat{j}-20\hat{k})\cdot (10\hat{i}-5\hat{j}-15\hat{k})}{\sqrt{25+100+400}\cdot \sqrt{100+25+225}}\]

\[=\frac{50-50+300}{\sqrt{525}\cdot \sqrt{350}}\]

\[\Rightarrow \] \[\cos \theta =\frac{1}{\sqrt{2}}\]

\[\therefore \] \[\theta ={{45}^{o}}\]