6. In Section 12.5, you learned that the distance from a point (ro, Yo, zo) to a plane ax+by+cz = d is |d – axo – byo – cz,l Va? + 62 + c2 Find the point on the graph of the surface S given by z = 2? + y? + 10 closest to the plane x + 2y – z = 0. Hint: on the surface S, z - x - 2y > 0.

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: A line I passes through the points A = (-1,0, 1) and B = (1, 1, 0) and is perpendicular to a plane…

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

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Q: 10. The distance between the point (3,-2,5) and the plane 2x+2y+z=5 is NONE

A: Given: The distance between (3,-2,5) and the plane 2x+2y+z=5

Q: 1. Find the equations of the planes that are exactly 4 units from the plane 2x-2y+z=6

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Q: A cardboard box without a lid is to have a volume of 10,976 cm³. Find the dimensions that minimize…

A: (a) We have to find the dimensions that minimize the amount of cardboard used. (b) We Find the…