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BITSAT 2012
Exam
BITSAT
Year
2012
Subject
Mathematics
Chapter
Three Dimensional Geometry

BITSAT 2012 · Mathematics · Three Dimensional Geometry

Find the coordinates of the point where the line joining the points...

Find the coordinates of the point where the line joining the points (2,-3,1) and (3,-4,-5) cuts the plane 2x+y+z=72 x+y+z=7

Options

  1. A(1,2,-7)
  2. B(1,-2,7)
  3. C(-1,-2,7)
  4. D(1,2,7)

Correct answer

B. (1,-2,7)

Step-by-step solution

The direction ratios of the line are 3−2,−4−(−3),−5−13-2,-4-(-3),-5-1 i.e. 1,-1,-6 Hence equation of the line joining the given points is x−21=y+3−1=z−1−6=r(\frac{x-2}{1}=\frac{y+3}{-1}=\frac{z-1}{-6}=r( say )) Coordinates of any point on this line are (r+2,−r−3,−6r+1)(r+2,-r-3,-6 r+1) If this point lies on the given plane 2x+y+z=72 x+y+z=7 then 2(r+2)+(−r−3)+(−6r+1)=7⇒r=−12(r+2)+(-r-3)+(-6 r+1)=7 \Rightarrow r=-1 Coordinates of any point on this line are (−1+2,−(−1)−3,−6(−1)+1)(-1+2,-(-1)-3,-6(-1)+1) i.e. (1,-2,7)
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