AP EAMCET · Maths · Vector Algebra
Given, \(\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and \(a\) unit vector \(\mathbf{c}\) are coplanar. If \(\mathbf{c}\) is perpendicular to a, then \(\mathbf{c}=\)
- A \(\pm \frac{1}{\sqrt{3}}(\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}})\)
- B \(\frac{1}{\sqrt{5}}(\hat{\mathbf{i}}-2 \hat{\mathbf{j}})\)
- C \(\frac{-1}{\sqrt{3}}(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})\)
- D \(\pm \frac{1}{\sqrt{2}}(-\hat{\mathbf{j}}+\hat{\mathbf{k}})\)
Answer & Solution
Correct Answer
(D) \(\pm \frac{1}{\sqrt{2}}(-\hat{\mathbf{j}}+\hat{\mathbf{k}})\)
Step-by-step Solution
Detailed explanation
Given, \(\begin{array}{r} \mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}} \\ \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}} \end{array}\) Let \(\mathbf{c}=x \hat{\mathbf{i}}+y \hat{\mathbf{j}}+z \hat{\mathbf{k}}\)…
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