1. (1 point) Consider the planes given by the equations 2x+3y-2z=3, x+y+3z=6. (a) Find a vector v parallel to the line of intersection of the planes. V= (b) Find the equation

of a plane through the origin which is perpendicular to the line of intersection of these two planes. This plane is. 2. (1 point) Find an equation for the plane containing the line in the xy- plane where y = 1, and the line in the xz-plane where z = 2. equation: 3. (1 point) (A) Find the parametric equations for the line through the point P =(3, -4,-2) that is perpendicular to the plane - 1x-4y+2z= 1. Use "t" as your variable, t=0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane. y=. Z= (B) At what point Q does this line intersect the yz-plane? Q=( 4. (1 point) Find the distance the point P(-6, -2, -1), is to the plane through the three points Q(-5, 0, 2), R(-8, -2, 1), and S(-4, -5, 1). 5. (1 point) Find a vector equation for the line through the point P =(3, 1, -1) and parallel to the vector v = (1, -3, -5). Assume r(0) = 3i+lj-lk and that v is the velocity vector of the line.. r(t)=i+ -j+. _k Rewrite this in terms of the parametric equations for the line. X = y= z = 6. (1 point) Rewrite the vector equation r(t) = (−3+5t)i+ (-4-2r)j+(1-1)k as the corresponding parametric equations for the line. x(t) y(t) z(1) 7. (1 point) Find the distance the point P(0,-4,5) is to the line through the two points Q(-5,-5,0), and R(-2,-7,2). 8. (1 point) Give vector parametric equation for the line through the point (-1,-3,2) that is parallel to the line (4+21,4-5r,1+41): L(t) = 9. (1 point) Give a vector parametric equation for the line through the point (-3,-4) that is perpendicular to the line (21-2,3): L(1) = .