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
$\mid \overrightarrow{ A }+\overrightarrow{ B }|$
$|\overrightarrow{ C }|^{2}=|\overrightarrow{ A }+\overrightarrow{ B }|^{2}$
$25=16+9+2 \times 4 \times 3 \cos \theta$
$\Rightarrow 25-25=24 \cos \theta$
$\Rightarrow \cos \theta=0$
$\Rightarrow \theta=90^{\circ}$