Question

If the magnitudes of vectors $\overrightarrow{A},\overrightarrow{B}$ and $\overrightarrow{C}$ are 4,3 and 5 units respectively and $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C},$ the angle between vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ is:

• A. ${\cos }^{-1}90^{\circ }$
• B. ${\cos }^{-1}\left(\frac{5}{16}\right)$
• C. ${\tan }^{-1}(5)$
• D. ${\tan }^{-1}\left(\frac{12}{5}\right)$

Answer 1

Answer: (A)

Given condition is that
$\overrightarrow{C}=\overrightarrow{A}+\overrightarrow{B}$
5 is the resultant or modulus of a vector
$\mid \overrightarrow{A}+\overrightarrow{B}|$
$|\overrightarrow{C}{|}^2=|\overrightarrow{A}+\overrightarrow{B}{|}^2$
$25=16+9+2\times 4\times 3\cos \theta$
$\Rightarrow 25-25=24\cos \theta$
$\Rightarrow \cos \theta =0$
$\Rightarrow \theta =90^{\circ }$