The Cartesian equation of the line passing through the point (-1,3,-2) and perpendicular to the lines x 1 = y 2 = z 3 and x+2 -3 = y-1 2 = z+1 5 is

Step-by-step solution

P=(-1,3,-2) Let dr 's or required line be (a, b, c) Dr's of line x 1 = y 2 = z 3 are (1,2,3) Given that required line perpendicular to above line a₁ a₂+b₁ b₂+c₁ c₂=0 a+2 b+3 c=0 Similarly required line perpendicular to x+2 -3 = y-1 2 = z+1 5 -3 a+2 b+5 c=0 On solving Eqs. (i) and (ii), we get aligned & a 10-6 = b -9-5 = c 2+6 & a 2 = b -7 = c 4 & aligned Required line is passing through (-1,3,-2) and having dr's (2,-7,4) x+1 2 = y-3 -7 = z+2 4