Looking for the solutions to share with my students, lto so I am not aware of this unit.

l. 9. Equations of Lines Review Determine the parametric, vector and scalar equations for the line passing through the points A(2,5) and 3(3, 1). Determine the vector equation of the line that is perpendicular to the line 4x y + 7 = 0 and passes through the point (5.3). Determine thex intercept of the line F = (2,1)+ t(7,3); t E R. Does the point (4, 2,3) lie on the line defined bythe parametric equations: x=10+2t y=113t z=6+t Determine the obtuse angle between the lines ll: 2x 5y + 1 = 0 and 12.x+3y7 =0. Determine the acute angle between the lines [1: (2,4,5) + t(2,1, 3); t E IR and (2: (1,1,5) + 5(1,5, 7); 5 E R. Prove if the following pairs of lines are parallel and distinct, perpendicular, coincident or none. (3) [1: F = (4,3) + t(3,4); t 6 IR [2: 8x6y14-20 (b) :1: F = (1,7,2) + t(2,5,4);t e 1R [2: 13 = (3,7,2) + t(5,6,5);t 6 IR Determine the vector equation of the line that passes through the point P(3,5,1) and is: (a) parallel to the y axis. (b) perpendicular to both 11: F = (1,2,7) + t(3, 2,5); t E R and [2:13 = (4, 17,23) + s(2,4,5); s 6 IR. Determine the intersection point of the following lines (if one exists). If not, state whether the lines are parallel and distinct or skew. (a) 11:5x3y+7=0 l2: 7x4y+8=0 (b) 1,: (2,1.5)+ t(5,4,3),t e IR I2: (5,13,4) + s(1,4,3), s 6 IR (a) 1,: F = (2,9, 4) + t(1,5,7}; t 2 IR x7 y 12. S Z+1 10. Determine the shortest distance from the point A(3,5) and the line 2x5y+1=0. 11. Determine the shortest distance from the point A(2,3,5) to the line F = (1,7,2) + t(6,5,2), t E R. Try each of the three methods and see if you get the same