A line goes through the point A (2,1,3). This line is also perpendicular to the two vectors U=i+j+k Determine the equation for this line, in both symmetric and parametric forms. V=2i-j-3k 8. Find the equation for a plane that contains 2 points: A(0,5, 0), B(0,9,1) and is parallel to the line with x=2+3t parametric equation L = y=3-2t. Put your final answer in the form ax+by+cz+d=0 z = 4+t Onicz r 7. Find the distance between these 2 parallel planes: (x+2y-2z=-3 x+2y-2z=3 02037 7 or 2000 E 6. Find the equation for the line that is passing through the points A(2,4,-3) and B (3,-1,1). Put the answer in parametric and symmetric form. Then determine the point where this line passes through the xy- plane. x=1-t 5. Turn in: Determine the point where the line y = -3+2t passes through z=t the plane x+y+z-4=0. And find the angle that this line makes with the plane using the dot product. You may express the angle relative to the vertical or horizontal, but be sure to be specific. af 4. Turn in: Find the equation for the plane that contains the 3 points: (1,2,1) (3,2,2) (4,-1,-1). Put your final answer in the form ax+by+cz+d=0 7 x=t 2. Turn in: Object A travels along the line defined by L =y=-t and Object B, along the line defined by z=1-t x=t-3 L = y=2t z=4t-1 Determine whether the 2 objects will cross or collide. And find the point of intersection (or collision). 3. Turn in: The symmetric equations for 2 lines are given as: [4: x = y+2 = -z+2 L: x-2=-y+1 = z+1 . Confirm that they are skew lines and then find the distance between them.