JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(\overrightarrow{\mathrm{a}}=3 \hat{i}-\hat{j}+2 \hat{k}, \overrightarrow{\mathrm{~b}}=\overrightarrow{\mathrm{a}} \times(\hat{i}-2 \hat{k})\) and \(\overrightarrow{\mathrm{c}}=\overrightarrow{\mathrm{b}} \times \hat{k}\). Then the projection of \(\overrightarrow{\mathrm{c}}-2 \hat{j}\) on \(\vec{a}\) is :
- A \(2 \sqrt{14}\)
- B \(\sqrt{14}\)
- C \(3 \sqrt{7}\)
- D \(2 \sqrt{7}\)
Answer & Solution
Correct Answer
(A) \(2 \sqrt{14}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \overrightarrow{\mathrm{b}}=\overrightarrow{\mathrm{a}} \times(\hat{\mathrm{i}}-3 \hat{\mathrm{k}}) \\ & =\left|\begin{array}{ccc} \hat{\mathrm{i}} & \hat{\mathrm{j}} & \hat{\mathrm{k}} \\ 3 & -1 & 2 \\ 1 & 0 & -2 \end{array}\right|=2 \hat{\mathrm{i}}+8…
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