If ( a ,   b ,   c ) is the image of the point ( 1 , 2 , - 3 ) in the line, x + 1 2 = y - 3 - 2 =…

If (a, b, c) is the image of the point (1,2,-3) in the line, x+12=y-3-2=z-1, then a+b+c is equal to:
  1. 2
  2. -1
  3. 3
  4. 1

Solution

R(-1+2r,3-2r,-r)

dr's of PR are (2-2 r,-1+2 r,-3+r)

Then,  2(2-2 r)+2(1-2 r)+1(3-r)=0

9-9r=0 ⇒ r=1

R(1,1,-1)

then  a+1=2 ,b+2=2 , c-3=-2 i.e., a=1,b=0, c=1

∴  a+b+c=2

 

Asked in: JEE Main 2020 (05 Sep Shift 1)

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