Question

The magnitude of one vector is double that of the other and the resultant of the two vectors is equal in magnitude with the magnitude of the bigger vector. The angle between the two vectors is:

• A. ${\cos }^{-1}\left(1/2\right)$
• B. ${\cos }^{-1}(-1/2)$
• C. ${\cos }^{-1}\left(1/4\right)$
• D. ${\cos }^{-1}(-1/4)$

Answer 1

Answer: (D)

${\cos }^{-1}(-1/4)$

Given, $\left|\overrightarrow{A}\right|=2\left|\overrightarrow{B}\right|,\left|\overrightarrow{R}\right|=\left|\overrightarrow{A}\right|=2\left|\overrightarrow{B}\right|$
$R^2=A^2+B^2+2AB\cos \theta {4B}^2={4B}^2+B^2+2\times 2B\times B\cos \theta or\cos \theta =\frac{-1}{4}or\theta ={\cos }^{-1}\left(\frac{-1}{4}\right)$