5. Find the equation of the plane which passes through the point (6,0,-2) and contains the...
Find an equation of the plane that passes through the point (9,4,0) and contains the line x = −4−t , y = −2+6 t , z = 4+8 t
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
Find an equation of a plane through the point (1, 5, 1) which is orthogonal to the line x=3+5t y=5-1t z=-1+4tin which the coefficient of x is 5.
Q4. (5 points). Find the equation of the plane that passes through the line of intersection of the two planes x - 2y = 3 and y- z = 0 and parallel to the line x = y - 1 = 2+1 Q5. (4 points). Find the distance from the point A(1,2,3) and the line 2+1 y-1 2 Q6. (4 points). Give the name and sketch the surface whose equation is given by x2 + 2y2 – 12y – z...
Find an equation of the plane. The plane through the point (3, 0, 1) and perpendicular to the line x = 6t, y = 2 − t, z = 9 + 4t
--1)+3y+2(z-4) 0 (9) Find an equation of the plane (a) through the point (2,0, 1) and perperndicular to the line a =3t, y 2- t,z3t+4 (b) passes through the point (1,-1,-1) parallel t the plane bz-y-z6 (c) passes through the point (3,5,-1) and contains the line a 4-t,y = -1+2t, z3t (d) passing through (-1,1,1), (0,0,2) and (3,-1,-2).
(a) Find symmetric equations for the line that passes through the point (4, -2, 6) and is parallel to the vector (-1, 3, -4) x+ 4-Y+ 2 3 z-6 -4 -(x +4) 3(y 2)-4(z +6). y+2 z-6 3 -(x-4) 3(y +2) -4(z- 6). o4-2-116 = Y - 2-z+6 3 (b) Find the points in which the required line in part (a) intersects the coordinate planes. 5 ,5,0 x ) point of intersection with xy-plane 10 7 point of intersection with...
Question 9: Plane through point and line A plane contains the point P(-1,2,3) and the line L(t), where L(t) is given by equation (2, 4t - 3,1 – 4t). Find the equation of this plane. Type in the equation of the plane with the accuracy of at least 3 significant figures for each coefficient 1 ) x + ( Dy+ ( )= / Save & Grade Save only
(1) (a) Find the equation of the line, Li, which passes through the points A : (4,y,z) = (0, -5, -3) and B : (x, y, z)=(3, 1,0). (b) Find the equation of the line, Ly, which passes through the points C:(x, y, z)=(-1, -3,2) and D: (x,y,z) = (4,3,6). (c) Show that L and Ly are not parallel lines. (d) Write the parametric equations for L, and L2, and then show that the lines Li and L2 do not...
1. 2. Find an equation for the plane that is perpendicular to the plane 2.1 + y + 2z = 1 and contains the line Lor=2+t, y = 1+ 4t, z = 1+ 4t. Find the equation of the tangent plane to the surface 2z - 12 = 0 at the point (2,0,2).