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TS EAMCET · Maths · Vector Algebra

If \(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), \(\mathbf{c}=-\hat{\mathbf{i}}+\hat{\mathbf{j}}-4 \hat{\mathbf{k}}\) and \(\mathbf{d}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\), then \((\mathbf{a} \times \mathbf{b}) \times(\mathbf{c} \times \mathbf{d})=\)

  1. A \(-7 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}\)
  2. B \(8 \hat{\mathbf{i}}-36 \hat{\mathbf{j}}+60 \hat{\mathbf{k}}\)
  3. C \(5 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}\)
  4. D \(-8 \hat{\mathbf{i}}-36 \hat{\mathbf{j}}+12 \hat{\mathbf{k}}\)
Verified Solution

Answer & Solution

Correct Answer

(B) \(8 \hat{\mathbf{i}}-36 \hat{\mathbf{j}}+60 \hat{\mathbf{k}}\)

Step-by-step Solution

Detailed explanation

If \(\mathbf{a} \times \mathbf{b}=\left|\begin{array}{ccc}\hat{\mathbf{i}} & \hat{\mathbf{j}} & \hat{\mathbf{k}} \\ 2 & 1 & -3 \\ 1 & -2 & 3\end{array}\right|\)…