TS EAMCET · Maths · Vector Algebra
Let \(\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \mathbf{b}=7 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}\), \(\mathbf{c}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\). The vector \(\mathbf{x}\) such that \(\mathbf{x} \cdot \mathbf{c}=60\) and perpendicular to both \(\mathbf{a}, \mathbf{b}\) is
- A \(14 \hat{i}-6 \hat{j}-12 \hat{k}\)
- B \(\hat{i}+34 \hat{j}+25 \hat{k}\)
- C \(4 \hat{i}-21 \hat{j}-12 \hat{k}\)
- D \(6 \hat{i}-6 \hat{j}+28 \hat{k}\)
Answer & Solution
Correct Answer
(B) \(\hat{i}+34 \hat{j}+25 \hat{k}\)
Step-by-step Solution
Detailed explanation
We have, \(\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \mathbf{b}=7 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, \mathbf{c}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\) Since, \(\mathbf{a} \perp \mathbf{x}\) and…
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