1/ Find parametric equation for the curve: a/ x^2= y^2/2 + z^2 and the plane z=1

Question

1/ Find parametric equation for the curve:

a/ x^2= y^2/2 + z^2 and the plane z=1

b/ x^2= y^2/2 + z^2 and the plane x=2

2/ Use the plane 2x-3z=7

a/ Describe all of intercepts of this plane

b/ Write a vector equation of a line that is orthogonal to this plane and has a y-intercept of 3

c/ Find the coordinate of the point that you foud in part b intersect the plance

d/ How far is the point (1,2, 3) from this plane ?

3/ Find the equation of a plane that include the intersection of the plane: x+y+z=1 and x= 2y+3z=1. Moreover, it also contains the intersection between the line: r(t)=< 1+t, 1-t, 2t> and r(s)= < 2-s,s,2>

Thanks

Explanation / Answer

D

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