Question

Find the vector equation of the line passing through the points A(2, 3, –1) and B(5, 1, 2).

Answer 1

Direction ratios of line AB are 5 – 2, 1 – 3, 2 + 1

i.e. 3, – 2, 3

∴ The line is parallel to `barb = 3hati - 2hatj + 3hatk`

∴ Its vector equation is `barr = bara + λbarb`

i.e. `barr = 2hati + 3hatj - hatk + λ(3hati - 2hatj + 3hatk)`