Question

If $| ⥂ \overrightarrow{A} + \overrightarrow{B} ⥂ | = | ⥂ \overrightarrow{A} ⥂ | + | ⥂ ⥂ \overrightarrow{B} ⥂ |$, then angle between \overrightarrow{A} and \overrightarrow{B}$ will be-

• A. (a)$90^{0}$
• A. (b)$120^{0}$
• A. (c)$0^{0}$
• A. (d)$60^{0}$

Answer 1

(c)

Resultant of two vectors $\overset{\rightarrow}{A}$ and $\overset{\rightarrow}{B}$ can be given by $\overset{\rightarrow}{R} = \overset{\rightarrow}{A} + \overset{\rightarrow}{B}$

$|\overset{\rightarrow}{R}| = |\overset{\rightarrow}{A} + \overset{\rightarrow}{B}| = \sqrt{A^{2} + B^{2} + 2AB\cos\theta}$

If $\theta = 0{^\circ}$ then $|\overset{\rightarrow}{R}| = A + B = |\overset{\rightarrow}{A}| + |\overset{\rightarrow}{B}|$