(I point) Let F=21+(z + y) j + (z _ y + z) k. (1+4t). y = 4 + 2t, z = _ (1+t). Let the line l be x =- (a) Find a point P-(zo, 30, zo) where F is parallel to 1. Find a point Q (which F and I are perpendicular. Q= and l are perpendicular Give an equation for the set of all points at which F and l are perpendicular. equation: (I point) Let F=21+(z...
Find the distance from the point with position vector y=[ 1,-3]| to the line through the origin parallel to y = [-2,4]. Give your answer rounded to 2 decimal places.
(1 point) Find the distance of the point (2,4, -4) from the line r(t) = (1 + 2t, 1 + 4t, 3 – 3t). Answer:
Find the line of intersection of the planes x + 2y + z = 9 and x - 2y + 3z = 13. x = -4t+ 7, y = and z = 2t + 2 x= -4t+9, y = 1 and z = 2t + 2 x = 4t + 7, y = tand z = 2t +2 x = -4t+ 7, y = ? and z = 2t - 2
(1 point) Let F = xi+ (x + y) 3+ (x – y+z) k. Let the line l be x = 4t – 3, y = — (5 + 4t), z = 2 + 4t. = (20, Yo, zo) where F is parallel to l. (a) Find a point P P= Find a point Q = (x1, Yı, z1) at which F and I are perpendicular. Q - Give an equation for the set of all points at which F...
Find the line of intersection of the planes x + 2y + z = 7 and x - 2y + 3z = 13. x = 4t+4, y = t and z = 2t + 3 x=-4t+4, y = t and z= 2t-3 x=-4t+ 7, y=t and z= 2t + 3 x=-4t +4, y = t and z = 2t + 3
2. Find distance from point S(-2, 3, 4) to the line x = 3 - 2t, y = –2 + 3t, 2 = 5 - 6t Write plane equation passing through point S and par- allel to the given line. Show calculation steps clear and cleanly.
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
4) Do the lines: L: x = 2t + 3, y = 3t – 2, z = 4t - 1 and L2 : x = 8 +6, y = 2s + 2, z = 2s + 5 intersect? If not provide a reason, if yes find the intersection point.
1) Show that two lines are skew x+1 y+2 z+3 4:x=y=z and L: +7=5 2) Find the general equation of the plane containing the point P (1,2,3 ) and L, . 3) Find the point Q-the point of intersection the plane found in 2) and the line L. 4) Find the distance from the point (1,-1,2) to the line Lą.