The equation of the plane containing the line x+1 -3 = y-3 2 = z+2 1 and the point (0,7,-7) is

Step-by-step solution

Let a, b, c be the direction cosines of the required plane. It contains the line x+1 -3 = y-3 2 = z+2 1 and passes through the point (0,7,-7) aligned & a ( x +1)+ b ( y -3)+ c ( z +2)=0 (1) & a (0+1)+ b (7-3)+ c (-7+2)=0 a +4 ~b -5 c =0 . aligned Also -3 a +2 ~b + c =0 From (2) and (3), we write a | array cc 4 & -5 2 & 1 array | = -b | array cc 1 & -5 -3 & 1 array | = c | array cc 1 & 4 -3 & 2 array | a 14 = b 14 = c 14 a = b = c =1 Hence eq. (1) becomes x+1+y-3+z+2=0 x+y+z=0