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4. Find the parametric equations for a line through a point (0,1,2) that (a). parallel to...
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) (A) Find the parametric equations for the line through the point P = (2, 3, 4) that is perpendicular to the plane 2x + 1 y + 3z 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. X= y- (B) At what point Q does this line intersect the yz-plane?
Find the equation of the plane through the point (-2,8,10) and parallel to the line x=1+t, y=2t, z=4-3t
Find the equation of the line that passes through the point (2,3,4) and is perpendicular to the plane 2x-y + 3z = 4 a. x=4+2t , y=2-t, z=7-3t b. x=2+2t , y=3-t, z=4+t c. x=2-2t , y=-3+t, z=4-3t d. x=-2+4t , y=5-2t, z=-2+6t e. another solution
(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=(
Find parametric equations of the line through the point (7,0, -3) that is parallel to the planes x - 8y + 6z = 0 and 8x + 8y - 2+ 6 = 0. x= 7+81, y = = 81,2 = -3 -1 x= 7+ 401, y = -491, z = -3 - 72t x = 7 - 401, y = 491,2= -3 + 72t x= 7+1, y = -81, z = -3 + 6t 0 x= 7-1, y = 81,2...
uestion 7[value16jp (a) Find parametric equations for the tangent line to the curve of intersection of the cvlinders y -r2 and z - r2 at the point (1, -1,1) (b) Find an equation for the osculating plane of the curve ア(t) 〈cos 3t, 4t, sin 3t) at the point (-1.4T,0). uestion 7[value16jp (a) Find parametric equations for the tangent line to the curve of intersection of the cvlinders y -r2 and z - r2 at the point (1, -1,1) (b)...
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.
Find parametric equations for the line through the points P(-1,-1,5) and Q(-5, -6,3). O A. x= - 4+1 y = -5t + 1 z= - 2t - 5 OB. X= - 4 - 1 y = -5t-1 z= -2t + 5 OC. x=t-4 y=t- 5 z= 5t-2 OD. x=t+4 y=t+ 5 z= 5t + 2
5. Find parametric equations for the line through the point (0, 1,2) that is orthogonal to the line x = 1 + t, y 1-t, 2t, and intersects this line. (Hint: Try drawing this scenario in two dimensions, ie. draw two orthogonal lines and a point on each line away from the intersection. How would you find the direction vector?)