8. Suppose n is the outward normal to the cone z =x + y² (for z> 0) and C is the intersection of the cone with the plane z = 1. The direction on C consistent with the orientation of the cone is (a) clockwise when seen from above. (c) clockwise when seen from below. (b) counterclockwise when seen from above.

Q: 1. The plane containing the point (1,-5,8) and orthogonal to the line given b x=-3+15t, y=14-t,…

A:

Q: Find the distance from the line x = 2 + t, y = 1 + t, z = (1/2) (1/2)t to the plane x + 2y + 6z =…

A:

Q: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: Select the graph of the function y = [2(x– 1)]²+1. Compare the graph of this function with the graph…

A: We need to compare the two graphs.

Q: 4. Calculate the perpendicular distance between the plane with axis intercepts P(4, 0, 0), Q(0, 3,…

A: Answer is: 0.53846153846153846 Solution is given below:

Q: Find an equation for a plane R at a distance 9 from a plane P with equation 2x + 2y - z = 3 .

A:

Q: b) Find the angle between the surfaces x² + y² + ² = 19 and 2 = 2 x² + y²-7 at the point (3, 1, 3):

A: