HW 3.5 - Lines & Planes 1. A particular linear graph can be described by the parametric equations x=4+2t, y=-1+3t Describe the line using (a) a vector equation (b) a single equation in x & y. 2. A line goes through the points (4,2,-3) & (6,1,5) Describe the line with (a) a vector equation (b) a system of parametric equations (c) a symmetric equation. 3. Find the equation of the plane through the point (4,8,1) with normal vector (-2,-3,5) 4. For the planes with equations 7x-2y+3z=4 & 3x-5y-2z=0 (a) Find the angle between them (b) find the equation of their line of intersection 5. Find the distance between the point (4,2,4) and the line (x,y,z) = (5,-2,2)+(3,2,3)t 6. Find the distance between the point (-9,2,3) and the plane 3x-6y+2z=4 7. [*] find the distance between the point (5,-3,3) and the plane through the point (4,8,1) with normal vector (-2,-3,5) 8. [**] find the equation of a line through the point (x0, y0) and perpendicular to the vector (a,b). (a) do it by first converting the perpendicular vector to a parallel vector (b) do it another way: use a method similar to the creation of the formula for planes in 3 dimensions (c) show that the two formulas are equal

est 4mm Hw 3-5 Lines 6:, Planes _ A particular linear graph can be described by the parametric equations x=4+1t_ y=-l+3t Describe the line using (a) a vector equation (b) a single equation in it St 5'. , A line goes through the points {4,2,3} ti {6,1,5} Describe the line with {a} a vector equation {h} a system of parametric equations {c} a synunetric equation. Find the equation of the plane through the point {4,3,1} with normal vector (-2,-3,S} _ For the planes with equations Tx-2v+32=4 dz Bot-5 v-22= (a) Find the angle between them (b) fmd the equation of their line of intersection _ Find the distance between the point {4,2,4} and the line {are} = {5,-2,1]-|-(3,2,3}t _ Find the distance between the point (-113) and the plane 3xv+2.z=4 _ [*] fmd the distance between the point (5,4,3) and the plane through the point {4,8, l] with normal vector {-2,-3,5) . ["] t'md the equation oFa line through the point (an, ya.) and perpendicular to the vector [a,b}. (a) do it by fn'st oonverting the perpendicular vector to a parallel vector {h} do it another way: use a method similar to the creation of the Formula for planes in 3 dimensions {c} show that the two Formulas are equal