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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
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Solution
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
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