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JEE Mains · Maths · STD 12 - 11. three dimension geometry

જો એક સમતલ \(P\) માં બે રેખાઓ \(\overrightarrow{ r }=\hat{ i }+\lambda(\hat{ i }+\hat{ j }), \lambda \in R\) અને \(\overrightarrow{ r }=-\hat{j}+\mu(\hat{j}-\hat{ k }), \mu \in R\) હોય તથા \(Q (\alpha, \beta, \gamma)\) એ બિંદુ \(M (1,0,1)\) થી સમતલ \(P\) પરના લંબનાં યામો હોય તો \(3(\alpha+\beta+\gamma)\) ની કિમત ...... થાય. 

  1. A \(6\)
  2. B \(8\)
  3. C \(5\)
  4. D \(10\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(5\)

Step-by-step Solution

Detailed explanation

Dr's normal to plane \(=\left|\begin{array}{ccc}i & j & k \\1 & 1 & 0 \\0 & 1 & -1\end{array}\right|=-\hat{i}+\hat{j}+\hat{k}\) Equation of plane \(-1(x-1)+1(y-0)+1(z-0)=0\) \(x-y-z-1=0\) Now \(\frac{\alpha-1}{1}=\frac{\beta-0}{-1}=\frac{\gamma-1}{-1}=-\frac{(1-0-1-1)}{3}\)…
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