TS EAMCET · Maths · Vector Algebra
If \(|\mathbf{a}|=1,|\mathbf{b}|=2\) and the angle between \(\mathbf{a}\) and \(\mathbf{b}\) is \(120^{\circ}\), then \(\{(\mathbf{a}+3 \mathbf{b}) \times(3 \mathbf{a}-\mathbf{b})\}^2\) is equal to
- A 425
- B 375
- C 325
- D 300
Answer & Solution
Correct Answer
(D) 300
Step-by-step Solution
Detailed explanation
\begin{aligned} & \therefore\{(\mathbf{a}+3 \mathbf{b}) \times(3 \mathbf{a}-\mathbf{b})\}^2 \\ & =\{3 \mathbf{a} \times \mathbf{a}-\mathbf{a} \times \mathbf{b}+9 \mathbf{b} \times \mathbf{a}-3 \mathbf{b} \times \mathbf{b}\}^2 \\ & =\{-10 \mathbf{a} \times \mathbf{b}\}^2 \\ &…
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