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Question
If the two lines `(x - 1)/2 = (y + 1)/3 = (z - 1)/4` and `(x - 3)/1 = (y - "m")/2` = z intersect at a point, find the value of m
Solution
(x1, y1, z1) = (1, -1, 1), (x2, y2, z2)
= (3, m, 0)
(1, 2, b3) = (2, 3, 4), (d1, d2, d3)
= (1, 2, 1).
`|(x-2 - x_1, y_2 - y_1, z_2 - z_1),("b"_1, "b"_2, "b"_3),("d"_1, "d"_2, "d"_3)|` = 0
`|(3 - 1, "m" + 1, 0 - 1),(2, 3, 4),(1, 2, 1)|` = 0
`|(2, "m" + 1, -1),(, 3, 4),(1, 2, 1)|` = 0
2(3 – 8) – (m + 1)(2 – 4) – 1(4 – 3) = 0
– 10 – (m + 1)(– 2) – 1(1) = 0
– 10 + 2m + 2 – 1 = 0
2m – 9 = 0
2m = 9
m = `9/2`
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