Question

If the line `(x + 1)/2 = (y - 5)/3 = (z - "p")/6` lies in the plane 3x – 14y + 6z + 49 = 0, then the value of p is ______.

Options

• 2

• 4

• 3

• –4

Answer 1

If the line `(x + 1)/2 = (y - 5)/3 = (z - "p")/6` lies in the plane 3x – 14y + 6z + 49 = 0, then the value of p is 4.

Explanation:

If the line `(x + 1)/2 = (y - 5)/3 = (z - "p")/6` lies in the plane, then (–1, 5, p) should satisfy the equation of a plane 3x – 14y + 6z + 49 = 0

∴ 3(–1) – 14(5) + 6(p) + 49 = 0

⇒ 6p = 24

⇒ p = 4