Question

If $|\overset{\rightarrow}{A} \times \overset{\rightarrow}{B}|$ = $\sqrt { 3 }$ $\overset{\rightarrow}{A}.\overset{\rightarrow}{B}$ then the value of $|\overset{\rightarrow}{A} + \overset{\rightarrow}{B}|$ is -

• A. (A² + B² +$\sqrt{3}$AB)^1/2
• B. (A² + B² + AB)^1/2
• C. $\left( A^{2} + B^{2} + \frac{AB}{\sqrt{3}} \right)^{1/2}$
• D. A + B

Answer 1

Answer: (B)

(A² + B² + AB)^1/2

Answer 2

Given that $|\overset{\rightarrow}{A} \times \overset{\rightarrow}{B}|$ = $\sqrt { 3 }$ $\overset{\rightarrow}{A}$.$\overset{\rightarrow}{B}$

AB sin q =$\sqrt{3}$ AB cosq

Ž tan q =$\sqrt{3}$

or q = $\frac{\pi}{3}$

\$|\overset{\rightarrow}{A} + \overset{\rightarrow}{B}|$

=$\sqrt{A^{2} + B^{2} + 2AB\cos\pi/3}$

$= \sqrt{A^{2} + B^{2} + AB}$