Question

Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line 5x – 25 = 14 – 7y = 35z.

Find the vector and the Cartesian equations of a line that passes through the point A(1, 2, –1) and parallel to the line 5x – 25 = 14 – 7y = 35z.

Answer 1

The equation of the line 5x − 25 = 14 − 7y = 35z can be re-written as

`(x-5)/(1/5) = (y -2)/(-1/7) = z/(1/35)`

`\implies (x - 5)/7 = (y-2)/(-5) = z/1`

Since the required line is parallel to the given line, so the direction ratios of the required line are proportional to 7, −5, 1.

The vector equation of the required line passing through the point (1, 2, −1) and having direction ratios proportional to 7, −5, 1 is 

`vecr = (hati + 2hatj - hatk) + lambda(7hati - 5hatj + hatk)`