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BITSAT 2011
Exam
BITSAT
Year
2011
Subject
Mathematics
Chapter
Three Dimensional Geometry

BITSAT 2011 · Mathematics · Three Dimensional Geometry

Gives the line (L: (x-1)/(3)=(y+1)/(2)=(z-3)/(-1) ) and the plane...

Gives the line (L: x−13=y+12=z−3−1\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-3}{-1}) and the plane (\pi: x-2 y-z=0). Of the following assertions, the only one that is always true is

Options

  1. AL is (\perp) to (\pi)
  2. BL lies in (\pi)
  3. CL is not parallel to (\pi)
  4. DNone of these

Correct answer

B. L lies in (\pi)

Step-by-step solution

Since 3(1)+2(−2)+(−1)(−1)=3−4+1=03(1)+2(-2)+(-1)(-1)=3-4+1=0 (\therefore) Given line is (\perp) to the normal to the plane i.e., given line is parallel to the given plane. Also, (1,−1,3)(1,-1,3) lies on the plane x−2y−z=0x-2 y-z=0 if 1−2(−1)−3=01-2(-1)-3=0 i.e., 1+2−3=01+2-3=0 which is true (\therefore) L lies in plane (\pi).
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