Question

Find the cartesian and vector equations of the line passing through A(1, 2, 3) and having direction ratios 2, 3, 7.

Answer 1

The vector equation of a line passing through point A(1, 2, 3) with direction ratios (2, 3, 7) is:

`r = (1hati + 2hatj + 3hatk) + lambda (2hati + 3hatj + 7hatk)`

`r = (1 + 2lambda) hati + (2 + 3lambda)hatj + (3 + 7 lambda)hatk`

Where λ is a scalar parameter.

The Cartesian equation of the line is:

`(x − 1)/2 = (y − 2)/3 = (z − 3)/7`