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Question
Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).
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Solution
The direction cosines of a line passing through the points P(x1, y1, z1) and Q(x2, y2, z2) are
`(x_2 - x_1)/"PQ", (y_2 - y_1)/"PQ", (z_2 - z_1)/"PQ"`
Here PQ = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2)`
= `sqrt((-1 - 2)^2 + (2 - 3)^2 + (4 - 5)^2)`
= `sqrt(9 + 1 + 1)`
= `sqrt(11)`
Hence D.C.'s are `+-((-3)/sqrt(11), (-1)/sqrt(11), (-1)/sqrt(11))` or `+-(3/sqrt(11), 1/sqrt(11), 1/sqrt(11))`
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