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

1 Answer
A. S. Adikesavan
Jul 27, 2016

#< 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 = 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#

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