TS EAMCET · Maths · Vector Algebra
Let \(\bar{a}=\bar{i}-\bar{j}+\bar{k}, \bar{b}=\bar{i}-2 \bar{j}-2 \bar{k}, \bar{c}=6 \bar{i}+3 \bar{j}-2 \bar{k}\) be three vectors. If \(\bar{d}\) is a vector perpendicular to both \(\bar{a}, \bar{b}\) and \(|\bar{d} \times \bar{c}|=14\), then \(|\bar{d} \cdot \bar{c}|=\)
- A 35
- B 70
- C 140
- D 105
Answer & Solution
Correct Answer
(B) 70
Step-by-step Solution
Detailed explanation
\(\bar{d} \propto \bar{a} \times \bar{b}\) \(\bar{a} \times \bar{b} = \begin{vmatrix} \bar{i} & \bar{j} & \bar{k} \\ 1 & -1 & 1 \\ 1 & -2 & -2 \end{vmatrix} = \bar{i}(2+2) - \bar{j}(-2-1) + \bar{k}(-2+1) = 4\bar{i} + 3\bar{j} - \bar{k}\) Let…
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