JEE Mains · Maths · STD 12 - 10. vector algebra
Let \(O\) be the origin and the position vector of the point \(P\) be \(-\hat{i}-2 \hat{j}+3 \hat{k}\). If the position vectors of the points \(A , B\) and \(C\) are \(-2 \hat{i}+\hat{j}-3 \hat{k}, 2 \hat{i}+4 \hat{j}-2 \hat{k}\) and \(-4 \hat{i}+2 \hat{j}-\hat{k}\) respectively then the projection of the vector \(\overline{O P}\) on a vector perpendicular to the vectors \(\overline{A B}\) and \(\overline{A C}\) is \(......\).
- A \(3\)
- B \(\frac{8}{3}\)
- C \(\frac{10}{3}\)
- D \(\frac{7}{3}\)
Answer & Solution
Correct Answer
(A) \(3\)
Step-by-step Solution
Detailed explanation
\(\overline{A B}=\overline{O B}-\overline{O A}\) \(=(2 \hat{i}+4 \hat{j}-2 \hat{k})-(-2 \hat{i}+\hat{j}-3 \hat{k})\) \(=4 \hat{i}+3 \hat{j}+\hat{k}\) \(\overline{A C}=\overline{O C}-\overline{O A}=-2 \hat{i}+\hat{j}+2 \hat{k}\)…
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