1.

Find the direction cosines of the sides of the triangle whose vertices are `(3, 5, 4)`, `( 1, 1, 2)`and `( 5, 5, 2)`.

Answer» Let `A(3,5,-4),B(-1,1,2) and C(-5,-5,-2)` are the given vertices of triangle `ABC`.
Direction cosines of AB can be given as,
`((x_2-x_1)/(AB),(y_2-y_1)/(AB),(z_2-z_1)/(AB)).`
Here,` AB = sqrt((-1-3)^2+(1-5)^2+(2-(-4))^2) = sqrt(16+16+36) = sqrt68`
`:.` Direction cosines of `AB = (-4/sqrt68,-4/sqrt68,6/sqrt68)`
Similarly, we can find the direction cosines of `AC` and `BC`.


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