Question

Choose correct alternatives:

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

Options

• 5

• 3

• 2

• –5

Answer 1

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

Explanation:

Given:

`(x + 1)/(2) = (y - m)/(3) = (z - 4)/(6)`

From this, a point on the line is

(−1, m, 4)

Plane equation:

3x − 14y + 6z + 49 = 0

3(−1) − 14(m) + 6(4) + 49 = 0

−3 − 14m + 24 + 49 = 0

70 − 14m = 0

14m = 70

m = 5