Question

The symmetric equation of lines 3x + 2y + z - 5 = 0 and x + y - 2z - 3 = 0, is

• A.
  
• B.
  
• C.
  
• D.
  

Answer 1

The correct option is C

Let a, b, c be the d.r.'s of required line
$\therefore$ 3a + 2b + c = 0 and a+ b - 2c = 0
$\frac{a}{-4-1}=\frac{b}{1+6}=\frac{c}{3-2}or\frac{a}{-5}=\frac{b}{7}=\frac{c}{1}$
In order to find a point on the required line we put z = 0 in the two given equation to obtain, 3x + 2y = 5 and x + y = 3. Solving these two equations, we obtain x = -1, y = 4.
$\therefore$ Cor - ordinates of point on required line are (-1, 4, 0). Hence required line is $\frac{x+1}{-5}=\frac{y-4}{7}=\frac{z-0}{1}$.