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AP EAMCET · Maths · Vector Algebra

If \(\bar{a}=2 \bar{i}-\bar{j}+6 \bar{k} ; \bar{b}=\bar{i}-\bar{j}+\bar{k}\) and \(\bar{c}=3 \bar{j}-\bar{k}\), then \(\bar{a} \times \bar{b}+\bar{b} \times \bar{c}+\bar{c} \times \bar{a}=\)

  1. A \(20 \overline{\mathrm{i}}+3 \overline{\mathrm{j}}-4 \overline{\mathrm{k}}\)
  2. B \(20 \overline{\mathrm{i}}-3 \overline{\mathrm{j}}+4 \overline{\mathrm{k}}\)
  3. C \(3 \overline{\mathrm{i}}+20 \overline{\mathrm{j}}-4 \overline{\mathrm{k}}\)
  4. D \(4 \overline{\mathrm{i}}+20 \overline{\mathrm{j}}-3 \overline{\mathrm{k}}\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(20 \overline{\mathrm{i}}+3 \overline{\mathrm{j}}-4 \overline{\mathrm{k}}\)

Step-by-step Solution

Detailed explanation

\( \bar{a} \times \bar{b} = \begin{vmatrix} \bar{i} & \bar{j} & \bar{k} \\ 2 & -1 & 6 \\ 1 & -1 & 1 \end{vmatrix} = ((-1)(1)-(6)(-1))\bar{i} - ((2)(1)-(6)(1))\bar{j} + ((2)(-1)-(-1)(1))\bar{k} = 5\bar{i} + 4\bar{j} - \bar{k} \)…