JEE Mains · Maths · STD 12 - 11. three dimension geometry
The length of the perpendicular drawn from the point \((2, 1, 4)\) to the plane containing the lines \(\vec r = \left( {\hat i + \hat j} \right) + \lambda \left( {\hat i + 2\hat j - \hat k} \right)\,\) and \(\vec r = \left( {\hat i + \hat j} \right) + \mu \left( { - \hat i + \hat j - 2\hat k} \right)\) is
- A \(\frac{1}{3}\)
- B \(\sqrt 3\)
- C \(\frac{1}{\sqrt 3}\)
- D \(3\)
Answer & Solution
Correct Answer
(B) \(\sqrt 3\)
Step-by-step Solution
Detailed explanation
Equation of plane containing both lines is \(\left| {\begin{array}{*{20}{c}} {x - 1}&{y - 1}&z\\ 1&2&{ - 1}\\ { - 1}&1&{ - 2} \end{array}} \right| = 0\) \((x-1)(-4+1)+(y-1)(1+2)+z(1+2)=0\) \(-3(x-1)+3(y-1)+3 z=0\) \(-x+1+y-1+z=0\)…
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