Question

How do you write the vector equation that passes through point (1,5) and parallel to <-7,2>?

Answer 1

`< x. y > = <1, 5>+k<-7, 2>`, where k is arbitrary.

Explanation:

The parametric form of any vector parallel to `<-7, 2>` is `k(-7, 2)>`.

If #r = <x, y> is the position vector to the point R(x, y) on the line

through P(1, 5) that is parallel to `<-7, 2>`, then the vector equation

of the line is

`< x. y > = <1, 5>+k<-7, 2>`, where k is arbitrary.

, using the addition law of vectors `OR=OP+PR`