JEE Mains · Maths · STD 12 - 11. three dimension geometry
A plane passes through the points \(A (1,2,3), B (2,3,1)\) and \(C (2,4,2)\). If \(O\) is the origin and \(P\) is \((2,-1,1) ,\) then the projection of \(\overline{ OP }\) on this plane is of length .... .
- A \(\sqrt{\frac{2}{7}}\)
- B \(\sqrt{\frac{2}{3}}\)
- C \(\sqrt{\frac{2}{11}}\)
- D \(\sqrt{\frac{2}{5}}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{\frac{2}{11}}\)
Step-by-step Solution
Detailed explanation
Normal to plane \(\vec{n}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ 1 & 1 & -2 \\ 0 & 1 & 1\end{array}\right|\) \(=3 \hat{i}-\hat{j}+\hat{k}\) \(\overline{O P}=2 \hat{i}-\hat{j}+\hat{k}\)…
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