If the lines x = a y + b , z = c y + d and x = a ′ z + b ′ ,    y = c ′ &#8201…

If the lines x=ay+b,z=cy+d and x=a′z+b′,  y=c′  z+d′ are perpendicular, then
  1. cc’+a+a’=0
  2. aa’+c+c’=0
  3. bb’+cc’+1=0
  4. ab’+bc’+1=0

Solution

Direction Ratios of the first line
i^j^k^1-a00c-1=a i^+j^+ck^ 
Hence, Direction Ratios of the first line are a, 1, c.
For Direction Ratios of the second line
i^j^k^10-a′01-c′=a′i^+c′j^+k^
Hence, Direction Ratios of the 2nd line =a′, c′, 1
Since, both the lines are perpendicular,
a.a′+c′+c=0

Asked in: JEE Main 2019 (09 Jan Shift 2)

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