Question

Two vectors of magnitude 3 units and 4 units respectively. What should be the angle between them if the magnitude of the resultant is 1 unit ?

• A. ${180}^o$
• B. ${90}^o$
• C. ${60}^o$
• D. $0$

Answer 1

Answer: (A)

${180}^o$

Given:

Magnitude of first vector, (say) $P=3$ units.

Magnitude of second vector, (say) $Q=4$ units.

Magnitude of resultant vector (say) $R=1$ unit.

Now, the magnitude of resultant vector R, is given by,

$R=\sqrt{(}{P}^2+Q^2+2PQ\cos \theta )$ ..................(1)

where, $\theta$ is the angle between two vectors.

Using the given values in equation (1), we get,

$1=\sqrt{(}{3}^2+4^2+2\left(3\right)\left(4\right)\cos \theta )$

$\therefore 1=\sqrt{(}25+24\cos \theta$ .....................(2)

Squaring both the sides of equation (2), we get,

$1=25+24\cos \theta$

$\therefore \cos \theta =\frac{-24}{24}$

$\therefore \cos \theta =-1$

$\therefore \theta ={180}^{\circ }$