ExamBro
ExamBro
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

  1. A 425
  2. B 375
  3. C 325
  4. D 300
Verified Solution

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 \\ &…