The Vector Equation which passes through point p(-4, 12) and parallel to q(14, -8) is r(t) = (14t-4, 12-8t).
What is Vector Equation?
A vector equation is an equation involving a linear combination of vectors with possibly unknown coefficients. Asking whether or not a vector equation has a solution is the same as asking if a given vector is a linear combination of some other given vectors.
Here, the line containing the vector q can be obtained by scaling q by an arbitrary scalar t. To make this line pass through the point p, translate this line by a vector p pointing from the origin to p.
So the line we want has equation
r(t) = qt + p
r(t) = (14, -8)t + (-4, 12)
r(t) = (14t - 4, 12-8t)
where t is any real number.
Thus, the Vector Equation which passes through point p(-4, 12) and parallel to q(14, -8) is r(t) = (14t-4, 12-8t).
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