Question

Direction cosines of the line `(x + 2)/2 = (2y - 5)/3`, z = -1 are ______ 

Options

• `4/5, 3/5, 0`

• `3/5, 4/5, 1/5`

• `-3/5, 4/5, 0`

• `4/5, -2/5, 1/5`

Answer 1

`underline(4/5, 3/5, 0)`

Explanation:

`(x + 2)/2 = (2y - 5)/3`, z = -1

∴ `(x + 2)/2 = (y - 5/2)/(3/2)`, z = -1

∴ `(x + 2)/4 = (y - 5/2)/3`, z = -1

∴ d.r.s of given line are 4, 3, 0

∴ d.c.s of the line are `4/sqrt(4^2 + 3^2), 3/sqrt(4^2 + 3^2), 0` i.e. `4/5, 3/5, 0`