TS EAMCET · Maths · Vector Algebra
Let \(\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\). If \(\mathbf{c}\) is \(\mathbf{a}\) unit vector such that \(\left[\begin{array}{lll}\mathbf{a} & \mathbf{b} & \mathbf{c}\end{array}\right]\) is maximum, then \(\mathbf{c}=\)
- A \(\frac{-\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\)
- B \(\frac{2 \hat{i}-\hat{j}-\hat{k}}{\sqrt{6}}\)
- C \(\frac{2 \hat{i}-\hat{j}+3 \hat{k}}{\sqrt{14}}\)
- D \(\frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}}{\sqrt{6}}\)
Answer & Solution
Correct Answer
(A) \(\frac{-\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}\)
Step-by-step Solution
Detailed explanation
Given that, \(\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\) and \(\quad \mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}\)…
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