AP EAMCET · Maths · Vector Algebra
If \(\mathbf{a}=\hat{i}+\hat{j}+\hat{k}, \mathbf{c}=\hat{j}-\hat{k}, \mathbf{a} \times \mathbf{b}=\mathbf{c}, \mathbf{a} \cdot \mathbf{b}=3\), then \(\mathbf{b}=\)
- A \(\frac{1}{3}(5 \hat{i}+2 \hat{j}+2 \hat{k})\)
- B \(\frac{1}{3}(2 \hat{i}+5 \hat{j}+2 \hat{k})\)
- C \(\frac{1}{3}(2 \hat{i}+2 \hat{j}+3 \hat{k})\)
- D \(\frac{1}{3}(2 \hat{i}+5 \hat{j}+5 \hat{k})\)
Answer & Solution
Correct Answer
(A) \(\frac{1}{3}(5 \hat{i}+2 \hat{j}+2 \hat{k})\)
Step-by-step Solution
Detailed explanation
Let \(\mathbf{b}=x \hat{i}+y \hat{j}+z \hat{k}\) If \(\mathbf{a} \times \mathbf{b}=\mathbf{c}\), then \(\mathbf{c}\) is perpendicular to both \(\mathbf{a}\) and \(\mathbf{b}\) \[ \begin{aligned} \mathbf{b} \cdot \mathbf{c} & =0 \\ y-z & =0 \\ y & =z...(i) \end{aligned} \] Also…
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