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TS EAMCET · Maths · Vector Algebra

If \(\bar{a}=\bar{i}-2 \bar{j}-2 \bar{k}\) and \(\bar{b}=2 \bar{i}+\bar{j}+2 \bar{k}\) are two vectors then \((\bar{a}+2 \bar{b}) \times(3 \bar{a}-\bar{b})=\)

  1. A \(2 \bar{i}+6 \bar{j}-5 \bar{k}\)
  2. B \(6 \bar{i}-2 \bar{j}+3 \bar{k}\)
  3. C \(14 \bar{i}+7 \bar{j}-5 \bar{k}\)
  4. D \(14 \bar{i}+42 \bar{j}-35 \bar{k}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(14 \bar{i}+42 \bar{j}-35 \bar{k}\)

Step-by-step Solution

Detailed explanation

\( (\bar{a}+2 \bar{b}) \times(3 \bar{a}-\bar{b}) = 3(\bar{a} \times \bar{a}) - (\bar{a} \times \bar{b}) + 6(\bar{b} \times \bar{a}) - 2(\bar{b} \times \bar{b}) \) \( = -7(\bar{a} \times \bar{b}) \)…