AP EAMCET · Maths · Vector Algebra
If \(\bar{a}=\bar{i}-2 \bar{j}-3 \bar{k}, \bar{b}=-2 \bar{i}+3 \bar{j}+4 \bar{k}, \bar{c}=5 \bar{i}-4 \bar{j}+3 \bar{k}\) and \(\bar{d}=3 \bar{i}+\bar{j}+5 \bar{k}\) are four vectors then \((\bar{a} \times \bar{b}) \times(\bar{c} \times \bar{d})=\)
- A \(18 \overline{\mathrm{i}}+6 \overline{\mathrm{j}}+30 \overline{\mathrm{k}}\)
- B \(8 \overline{\mathrm{i}}-3 \overline{\mathrm{j}}+8 \overline{\mathrm{k}}\)
- C \(19 \overline{\mathrm{i}}-5 \overline{\mathrm{j}}+21 \overline{\mathrm{k}}\)
- D \(27 \overline{\mathrm{i}}-8 \overline{\mathrm{j}}+29 \overline{\mathrm{k}}\)
Answer & Solution
Correct Answer
(A) \(18 \overline{\mathrm{i}}+6 \overline{\mathrm{j}}+30 \overline{\mathrm{k}}\)
Step-by-step Solution
Detailed explanation
\( \bar{a} \times \bar{b} = \begin{vmatrix} \bar{i} & \bar{j} & \bar{k} \\ 1 & -2 & -3 \\ -2 & 3 & 4 \end{vmatrix} = \bar{i}(-8+9) - \bar{j}(4-6) + \bar{k}(3-4) = \bar{i} + 2\bar{j} - \bar{k} \)…
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