Question

If the line `(x - 1)/2 = (y + 1)/3 = z/4` lies in the plane 4x + 4y – kz = 0, then the value of k is ______.

पर्याय

• 4

• 5

• 6

• 7

Answer 1

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

Explanation:

The d.r's of the given line are 2, 3, 4 and d.r's of the normal to the given plane are 4, 4, –k

Since the line is in the plane, it is perpendicular to the normal to the plane.

∴ (2)(4) + (3)(4) + (4)(–k) = 0

∴ 8 + 12 – 4k = 0

∴ 4k = 20

∴ k = 5