Find the point(s) of intersection of the line x = 1 – t, y = t, z =1– 2t - and the paraboloid z = 8 – x2 – y².

Q: Find the point on the plane x + 2y + 3z = 13 closest to the point (1, 1, 1).

A: Given plane is We need to find the point on the plane closest to

Q: Find the point at which the line (-3, 4, 2) +t(-4, 3, 1) intersects the plane -4x + y – 5z = 76.

A:

Q: Find the point on the plane x+y+z=-46 that is closest to the point (1,1,1).

A:

Q: Find the intersection of the line r(t) = 3t + 2, 1, −7t and the plane 2x − 3y + z = 5.

A: r(t)=3t+2, 1, -7t and the plane 2x-3y+z=5

Q: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the…

A: Direction ratios of normal to plane 2x - y + 2z =-2  are <2,-1,2>, since line is normal to…

Q: Find the point at which the line (1, 2, 3) + t(5, 1, 1) intersects the plane -4x - 4y + 4z = -160.

A: Any point on the line <1, 2, 3> + t<5, 1, 1> can be expressed as         (1 + 5t, 2 + t,…