Math: Equations of Line in a Plane

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I'm stuck on these questions. Can you please show me a step by step solution?


20) For each of the following, find a normal vector, a direction vector, and a point of each line.

Note, normal vector means perpendicular to the direction vector.

a) 3x - 6y = 14

TEXTBOOK ANSWER:
normal vector = (1 , -2)
direction vector = (2 , 1)
point on the line = [(14/3) , 0]




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21) Find vector, parametric, and symmetric equations of the following lines.

a) -4x + 6y + 9 = 0

TEXTBOOK ANSWER:
Vector Equation -> r = [0 , (-3/2)] + t(3 , 2)
Parametric Equation -> x = 3t and y = 2t - (3/2)
Symmetric Equation -> (x/3) = [y + (3/2)] / 2

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