Write a vector equation of the line that passes through point P(1,5) and is parallel to a = -7,2). Then write parametric equations of
the line.

Vector equation of the line ⇒ (x-1 , y-5) = t(-7,2)

Parametric equations ⇒ x = 1 - 7t  and  y = 5 + 2t

Step-by-step explanation:

Let the line L through (x,y) and through point P(1,5) and is parallel to a = (-7,2)

so, the vector equation of the line will be:

(x,y) - (1,5) = t(-7,2)

∴ (x-1 , y-5) = t(-7,2)

The parametric equations of the line will be:

x - 1 = -7t ⇒ x = 1 - 7t

y - 5 = 2t ⇒ y = 5 + 2t

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