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Question: If \(|\mathbf{a}| = 3,|\mathbf{b}| = 4\) and the angle between **a** and **b** be \(120^{o}\), then ...

If ∣a∣=3,∣b∣=4|\mathbf{a}| = 3,|\mathbf{b}| = 4 and the angle between a and b be 120o120^{o}, then ∣4a+3b∣=|4\mathbf{a} + 3\mathbf{b}| =

A

25

B

12

C

13

D

7

Answer

12

Explanation

Solution

∣4a+3b∣=(4a+3b).(4a+3b)|4\mathbf{a} + 3\mathbf{b}| = \sqrt{(4\mathbf{a} + 3\mathbf{b}).(4\mathbf{a} + 3\mathbf{b})}

=16∣a∣2+9∣b∣2+24a.b= \sqrt{16|\mathbf{a}|^{2} + 9|\mathbf{b}|^{2} + 24\mathbf{a}.\mathbf{b}}

=144+144+24×3×4×(−12)=12.= \sqrt{144 + 144 + 24 \times 3 \times 4 \times \left( \frac{- 1}{2} \right)} = 12.