WBJEE · Maths · Vector Algebra
If \(\vec{a}=\hat{i}+\hat{j}-\hat{k}, \vec{b}=\hat{i}-\hat{j}+\hat{k}\) and \(\vec{c}\) is unit vector perpendicular to \(\vec{a}\) and coplanar with \(\vec{a}\) and \(\vec{b}\), then unit vector \(\vec{d}\) perpendicular to both \(\vec{a}\) and \(\vec{c}\) is
- A \(\pm \frac{1}{\sqrt{6}}(2 \hat{i}-\hat{j}+\hat{k})\)
- B \(\pm \frac{1}{\sqrt{2}}(\hat{j}+\hat{k})\)
- C \(\pm \frac{1}{\sqrt{6}}(\hat{i}-2 \hat{j}+\hat{k})\)
- D \(\pm \frac{1}{\sqrt{2}}(\hat{j}-\hat{k})\)
Answer & Solution
Correct Answer
(B) \(\pm \frac{1}{\sqrt{2}}(\hat{j}+\hat{k})\)
Step-by-step Solution
Detailed explanation
\(\because \overrightarrow{\mathrm{d}}\) is normal to the plane of \(\overrightarrow{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\) \(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}\) or…
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