JEE Mains · Maths · STD 12 - 11. three dimension geometry
Let the position vectors of two points \(P\) and \(Q\) be \(3 \hat{ i }-\hat{ j }+2 \hat{ k }\) and \(\hat{ i }+2 \hat{ j }-4 \hat{ k },\) respectively. Let \(R\) and \(S\) be two points such that the direction ratios of lines \(PR\) and \(QS\) are \((4,-1,2)\) and \((-2,1,-2),\) respectively. Let lines \(PR\) and \(QS\) intersect at \(T\). If the vector \(\overline{ TA }\) is perpendicular to both \(\overline{ PR }\) and \(\overline{ QS }\) and the length of vector \(\overline{ TA }\) is \(\sqrt{5}\) units, then the modulus of a position vector of \(A\) is
- A \(\sqrt{482}\)
- B \(\sqrt{171}\)
- C \(\sqrt{5}\)
- D \(\sqrt{227}\)
Answer & Solution
Correct Answer
(B) \(\sqrt{171}\)
Step-by-step Solution
Detailed explanation
\(P (3,-1,2)\) \(Q (1,2,-4)\) \(\overline{ PR } \| 4 \hat{ i }-\hat{ j }+2 \hat{ k }\) \(\overline{ QS } \|-2 \hat{ i }+\hat{ j }-2 \hat{ k }\) dr's of normal to the plane containing \(P , T \) and \(Q\) will be proportional to :…
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