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Question: If \| \(\overset{\rightarrow}{A}\) × \(\overset{\rightarrow}{B}\)\| = \| \overset{\rightarrow}{A}\( ...

If | A→\overset{\rightarrow}{A} × B→\overset{\rightarrow}{B}| = | \overset{\rightarrow}{A}..\overset{\rightarrow}{B}thenthevalueof∥ then the value of \|\overset{\rightarrow}{A}++\overset{\rightarrow}{B}$| is –

A

(a) (A2 + B2 + 3 \sqrt{3}AB)1/2

A

(b) (A2 + B2 + AB)1/2

A

(c) (A2+B2+AB3)1/2\left( A^{2} + B^{2} + \frac{AB}{\sqrt{3}} \right)^{1/2}

A

(d) A + B

Explanation

Solution

(b)

|A→\overset{\rightarrow}{A} × B→\overset{\rightarrow}{B}| = 3\sqrt{3} A→\overset{\rightarrow}{A}.B→\overset{\rightarrow}{B}

Ž AB sin q = 3\sqrt{3} AB cos q

Ž tan q = 3\sqrt{3} Ž q = π3\frac{\pi}{3}

\ |A→\overset{\rightarrow}{A} + B→\overset{\rightarrow}{B}| = A2+B2+2ABcos⁡(π3)\sqrt{A^{2} + B^{2} + 2AB\cos\left( \frac{\pi}{3} \right)}

= A2+B2+AB\sqrt{A^{2} + B^{2} + AB}