Where does the line through (1, 0, 1) and (5, -3,5) intersect the plane x +...
The line k goes through the point Q(-3,5) and is perpendicular to the line g: x - 3y - 22 = 0. Where do the angle bisectors of lines g and k intersect the line AB when A = (-3,3) and B = (10,3)?
where does the line y=x+30 intersect the parabola y=6x^2
5 and 6 please 5) Given the surface f(x, y, z) = 0 or z = f(x,y), find the tangent plane at P. a) z2 – 2x2 – 2y2 = 12 @ P=(1,-1,4) b) f(x,y) = 2x - 3xy3 @ 12,-1) c) f(x,y) = sin(x) @ (3,5) 6) Find an equation of the tangent plane and the equation of the normal line to surface f(x..zb=0 @P x2 + y2 + z2 = 9 P = (2,2,1)
--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).
Let L be the line passing through the point P(1,5, -2) with direction vector d=[0,-1, 0]T, and let T be the plane defined by x–5y+z = 22. Find the point Q where L and T intersect. Q=(0,0,0)
Determine whether the line x = 7 – 4t, y = 3 + 6t, z = 9 + 5t and the plane 4x + y + 2z = 17 intersect or are parallel. If they intersect, then find the point of intersection
24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x, y, z] = [2,-2, 0] + r[2 kx+Zy-4: = 12. -3] is parallel to the plane (2 marks) 24. By analyzing the normals, determine if the three planes intersect in a point. π1: x-5y + 2z-10-0 (2 marks) 25. Find the value of k so that the line [x,...
Find the equation for the plane through Po(-1, -7,4) perpendicular to the following line. x= - 1+t, y= - 7+ 3t, z = -5t, -o0<t<00 The equation of the plane is 0.
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
0 intersect only at (0,0) g(r)at z arctan(3z) Show that the graph y f(x) and its tangent line y po Consider the ftunction f(x) Intermediate steps: 1) The lIne tangent to y f(x)atz -0isy g(x) where g(r) 9(a)- 2Let H(x) f(x) - 9(x) The derivative ot H (x)s H'(z) = which is zero only when x = Rolle's theorem to H (x) on the interval [ri, 0]. Get a contradiction. 4) Now assume that we have zp O where f(2)-9(T2)...