1-Find the distance (correct to two decimal places) between the given parallel p

Question

1-Find the distance (correct to two decimal places) between the given parallel planes.
(6x+7y-2z=10) and (12x+14y-4z=60).

2-Find an equation for the surface consisting of all points that are equidistant from the point (0,-5,0) and the plane y = 5.

3-Find the center and radius of the sphere;((x^2)+6x-8+(y^2)-8y+(z^2)-8z=0).

4-Find an equation of the plane with x-intercept = 7, y-intercept = 6 and z-intercept = 3.

5-Find the unit vectors that are perpendicular to the tangent line to the curve (y=3x^2)at the point (1,3).

Explanation / Answer

a)20/sqrt(89) = 2.12

b) y=0

c) centre (-3,4,4) radius = sqrt(41)

d)x/7 +y/6 +z/3 =2

e)y= -x/6 +19/6

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