JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\overrightarrow{\mathrm{a}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=((\overrightarrow{\mathrm{a}} \times(\hat{\mathrm{i}}+\hat{\mathrm{j}})) \times \hat{\mathrm{i}}) \times \hat{\mathrm{i}}\). Then the square of the projection of \(\vec{a}\) on \(\vec{b}\) is :
- A \(\frac{1}{5}\)
- B \(2\)
- C \(\frac{1}{3}\)
- D \(\frac{2}{3}\)
Answer & Solution
Correct Answer
(B) \(2\)
Step-by-step Solution
Detailed explanation
\(\vec{a} \times(\hat{i}+\hat{j})=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 2 & 1 & -1 \\ 1 & 1 & 0\end{array}\right|\) \( =\hat{i}-\hat{j}+\hat{k} \) \( (\vec{a} \times(\hat{i} \times \hat{j})) \times \hat{i}=\hat{k}+\hat{j} \)…
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