JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\bar{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}\) and \(\vec{c}=\hat{j}-\hat{k}\) be three vectors such that \(\vec{a} \times \vec{b}=\vec{c}\) and \(\vec{a} \cdot \vec{b}=1\). If the length of projection vector of the vector \(\vec{b}\) on the vector \(\vec{a} \times \vec{c}\) is \(l\), then the value of \(3l^{2}\) is equal to \(.....\)
- A \(3\)
- B \(1\)
- C \(2\)
- D \(9\)
Answer & Solution
Correct Answer
(C) \(2\)
Step-by-step Solution
Detailed explanation
\(\vec{a} \times \vec{b}=c\) Take Dot with \(\overrightarrow{\mathrm{c}}\) \((\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}) \cdot \overrightarrow{\mathrm{c}}=|\overrightarrow{\mathrm{c}}|^{2}=2\) Prokection of \(\overrightarrow{\mathrm{b}}\) on…
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