Question

Given $|{\overrightarrow{A}}_{1}| = 2$, $|{\overrightarrow{A}}_{2}| = 3$ and $|{\overrightarrow{A}}_{1} + {\overrightarrow{A}}_{2}| = 3$,

then$({\overrightarrow{A}}_{1} + 2{\overrightarrow{A}}_{2})$.$(3{\overrightarrow{A}}_{1} - 4{\overrightarrow{A}}_{2})$ is-

• A. – 64
• B. 60
• C. – 62
• D. None of these

Answer 1

Answer: (A)

– 64

Answer 2

$({\overrightarrow{A}}_{1} + 2{\overrightarrow{A}}_{2})$. $(3{\overrightarrow{A}}_{1} - 4{\overrightarrow{A}}_{2})$

= $3|{\overrightarrow{A}}_{1}|^{2} + \mspace{6mu} 2|{\overrightarrow{A}}_{1}||{\overrightarrow{A}}_{2}|\cos\theta - 8|{\overrightarrow{A}}_{2}|^{2}$=

$(|{\overrightarrow{A}}_{1}|^{2} + \mspace{6mu} 2|A_{1}||{\overrightarrow{A}}_{2}|\cos\theta + 8|{\overrightarrow{A}}_{2}|^{2})$ + $2|{\overrightarrow{A}}_{1}|^{2} - 9|{\overrightarrow{A}}_{2}|^{2}$

= 3² + 2 × 2² – 9 × 3² = 9 + 8 – 81 = – 64