Question

Two vectors of magnitudes 8 and 6 are acting at a point so as to produce a resultant of magnitude 10. The angle between the two vectors is:

• A. $co{s}^{-1}(\frac{3}{4})$
• B. $co{s}^{-1}(\frac{4}{3})$
• C. $co{s}^{-1}(\frac{7}{5})$
• D. ${90}^0$

Answer 1

The correct option is D ${90}^0$

The resultant of two vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ is given by:

$R=\sqrt{P^2+Q^2+2PQ\cos \theta }$

Where P and Q are magnitudes of two vectors and $\theta$ is the angle between two vectors

Here $\theta =?$, $P=8Q=6R=10$

Therefore,

$10=\sqrt{8^2+6^2+2\times 8\times 6\cos \theta }$

$100=64+36+96\cos \theta$

$100=100+96\cos \theta$

$100-100=96\cos \theta$

$cos\theta =0$

$cos\theta =\cos 90$

$\theta ={90}^0$