JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\vec{a}=\hat{i}-\hat{j}+2 \hat{k}\) and \(\vec{b}\) be a vector such that \(\vec{a} \times \vec{b}=2 \hat{i}-\hat{k}\) and \(\vec{a} \cdot \vec{b}=3\). Then the projection of \(\vec{b}\) on the vector \(\vec{a}-\vec{b}\) is :-
- A \(\frac{2}{\sqrt{21}}\)
- B \(2 \sqrt{\frac{3}{7}}\)
- C \(\frac{2}{3} \sqrt{\frac{7}{3}}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(A) \(\frac{2}{\sqrt{21}}\)
Step-by-step Solution
Detailed explanation
\(\vec{a}=\hat{i}-\hat{j}+2 \hat{k}\) \(\vec{a} \times \vec{b}=2 \hat{i}-\hat{k}\) \(\vec{a} \cdot \vec{b}=3\) \(|\vec{a} \times \vec{b}|^{2}+|\vec{a} \cdot \vec{b}|^{2}=|\vec{a}|^{2} \cdot|\vec{b}|^{2}\) \(5+9=6|\vec{b}|^{2}\) \(|b|^{2}=\frac{7}{3}\)…
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