AP EAMCET · Maths · Three Dimensional Geometry
If \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{c}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\) then the magnitude of the projection on \(\mathbf{c}\) of a unit vector that is perpendicular to both \(\mathbf{a}\) and \(\mathbf{b}\) is
- A \(\frac{1}{\sqrt{29} \sqrt{3}}\)
- B \(\frac{1}{\sqrt{6}}\)
- C \(\frac{1}{\sqrt{58}}\)
- D \(\frac{3}{\sqrt{29}}\)
Answer & Solution
Correct Answer
(C) \(\frac{1}{\sqrt{58}}\)
Step-by-step Solution
Detailed explanation
Given vectors are \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}} \text { and } \mathbf{c}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}\) Then,…
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