(1 pt) (A) Find the parametric equations for the line through the point P = (2,...
(1 point) (A) Find the parametric equations for the line through the point P = (-4, 4, 3) that is perpendicular to the plane 4.0 - 4y - 4x=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. (B) At what point Q does this line intersect the yz-plane? Q=(
please answer both (12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0 (12(8 pts) Find parametric equations of the line through the point (2,...
(1 pt) Find a vector equation for the line through the point P = (1, -2, 3) and parallel to the vector v = (-3, 2, -3). Assume r(0) = li – 2 + 3k and that v is the velocity vector of the line.. r(t) = i + j+ Rewrite this in terms of the parametric equations for the line. X < N
Q4 (8 points) (a) Find parametric equations to the line passing through the point A(5,-2,9) and perpendicular to the plane 3x - y - 6x + 2 = 0 (b) Find two planes that intersect along the line.
Q4 (8 points) (a) Find parametric equations of the line passing through the point A(5,-2,9) and perpendicular to the plane 33 - Y --- 62 +2 = 0. (b) Find two planes that intersect along the line
Q4 (8 points) (a) Find parametric equations of the line passing through the point A(5,-2,9) and perpendicular to the plane 3.x - y-6z+ 2 = 0. (b) Find two planes that intersect along the line.
4. Find the parametric equations for a line through a point (0,1,2) that (a). parallel to the plane x + y + z = 2, and (b). perpendicular to the line T = 1+t, y = 1 –t, z = 2t (Answer: x = 3t, y=1-t, 2 = 2 - 2t)
4) Find parametric equations for the line through the point P(3,6,0) and perpendicular to the plane 3x + 6y + 4z = 3 | | | wold moltoupato Carth
Find a vector equation and parametric equations for the line segment that joins P to Q. (D |-1+2-) 1 P(0, -1, 4) 4 -t.2 3 t. r(t) 4 vector equation X 7 4 t.2 3 1 - t. (x(t), y(t), z(t)) 4 X - parametric equations 2 If two objects travel through space along two different curves, it's often important to know whether they will collide. (Will a missile hit its moving target? Will two aircraft collide?) The curves might...
Question 12 Find parametric equations for the line of intersection of the planes - 2y+z= 1 and 2x + y - 3x = -3. Does the line L intersect the plane 2x - y - 3x = 1? If so, at what point? Note: This is the review exercise at the end of Lecture 2.