AP EAMCET · Maths · Vector Algebra
Given three vectors \(\mathbf{a}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(\mathbf{c}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}\), a vector in the plane of \(\mathbf{b}\) and \(\mathbf{c}\) whose projection on \(\mathbf{a}\) is of magnitude \(\sqrt{\frac{2}{3}}\) is
- A \(-2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+5 \hat{\mathbf{k}}\)
- B \(2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\)
- C \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+5 \hat{\mathbf{k}}\)
- D \(2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\)
Answer & Solution
Correct Answer
(A) \(-2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+5 \hat{\mathbf{k}}\)
Step-by-step Solution
Detailed explanation
Given three vectors are \(\begin{aligned} \mathbf{a} & =2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}} \\ \text {and } \quad \mathbf{c} & =\hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}} \end{aligned}\)…
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