In: Math
1. a.) determine vector and parametric equations for the line through the point A(2, 5) with direction vector = (1, −3).
b.)Determine a vector equation for the line through the points (-1, 4) and (2, -1).
c.) Determine parametric equations for the line through (-2, 3) and parallel to the line with vector equation = (−2, 1) + t(6, 4).
d .) A line passes through the point (-4, 1) and is perpendicular to the line with parametric equations x = -2 -3t, y = 1 + 2t. Find vector and parametric equations for the line.
e.) Find vector and parametric equations for the line with equation 2x + y + 3 = 0.
f.) Determine a scalar equation for the line that passes through the point (-1, 5) and has direction vector = (1, −3).
g.) Determine parametric equations for the line with scalar equation 4x – y + 5 = 0.
h.) Determine a scalar equation for the line with vector equation = (−3, 1) + t(2, 5).
i.) A line passes through the point (1, -4) and is perpendicular to the line 3x + 2y – 6 = 0. Determine a scalar equation for the line.
j.) Use a vector solution to show that a scalar equation for the line through the points P1(x1, y1) and P2(x2, y2) is