Question

Equation of a plane which passes through the point of intersection of lines$\frac{x - 1}{3} = \frac{y - 2}{1} = \frac{z - 3}{2}$ and

$\frac{x - 3}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}$and at greatest distance from the point (0, 0, 0) is

• A. 4x + 3y + 5z = 25
• B. 4x + 3y + 5z = 50
• C. 3x + 4y + 5z = 49
• D. x + 7y – 5z = 2

Answer 1

Answer: (B)

4x + 3y + 5z = 50

Answer 2

Let a point (3l + 1, l + 2, 2l + 3) of the first line also lies on the second line

Then$\frac{3\lambda + 1 - 3}{1} = \frac{\lambda + 2 - 1}{2} = \frac{2\lambda + 3 - 2}{3}$

Ž l = 1

hence the point of intersection P of the two lines is (4, 3, 5)

Equation of plane perpendicular to OP where O is (0, 0, 0) and passing through P is

4x + 3y + 5z = 50