Question

The angle between the two vectors $\overrightarrow{A}=3\hat{i}+4\hat{j}+5\hat{k}$ and $\overrightarrow{B}=3\hat{i}+4\hat{j}-5\hat{k}$ will be:

• A. ${90}^o$
• B. $0^o$
• C. ${60}^o$
• D. ${45}^o$

Answer 1

The correct option is A ${90}^o$

$\overrightarrow{A}=3i+4j+5k$

$\overrightarrow{B}=3i+4j-5k$

$\cos \theta =\frac{\overrightarrow{A}\cdot \overrightarrow{B}}{|\overrightarrow{A}|\times |\overrightarrow{B}|}$

Taking dot product

$\overrightarrow{A}\cdot \overrightarrow{B}=(3\times 3)+(4\times 4)+(5\times -5)=9+16-25=0$

$\cos \theta =\frac{0}{|\overrightarrow{A}|\times |\overrightarrow{B}|}=0$

$\Rightarrow \theta =\cos 0=\frac{\pi }{2}={90}^o$