Question

Find the angle between $\overrightarrow{A}=3\hat{i}+4\hat{j}$ and $\overrightarrow{B}=12\hat{i}+5\hat{j}$.

• A. ${\cos }^{-1}\frac{65}{56}$
• B. ${\cos }^{-1}\frac{56}{65}$
• C. ${\sin }^{-1}\frac{65}{56}$
• D. ${\cos }^{-1}\frac{53}{56}$

Answer 1

The correct option is B ${\cos }^{-1}\frac{56}{65}$

$\text{We have}\cos \theta =\frac{\overrightarrow{A}.\overrightarrow{B}}{AB}=\frac{(3\hat{i}+4\hat{j}).(12\hat{i}+5\hat{j})}{\sqrt{3^2+4^2}\sqrt{{12}^2+5^2}}$
$\cos \theta =\frac{36+20}{5\times 13}=\frac{56}{65}$
$\theta ={\cos }^{-1}\frac{56}{65}$