Question

Find the vector equation of the line passing through the point (2, 3, −5) and making equal angles with the co-ordinate axes. 

Answer 1

Given α = β = γ

Now, cos² α + cos² β + cos² β = 1

∴ 3 cos² α = 1      ...[∵ α = β = γ]

or, cos² α = `1/3`

or, cos α = ±`1/sqrt3`

Thus, cos α = cos β = cos γ = ±`1/sqrt3 = l = m = n`

Let required equation of line is  `overset->r = overset->a + kvecb`

Here, `overset->a = 2hat i + 3 hat j - 5 hat k`

`overset->b = ± 1/sqrt3 (hat i + hat j + hat k)`

Thus, required equation is  `overset->r = (2hat i + 3 hat j - 5 hat k) ± 1/sqrt3 (hat i + hat j + hat k)`