important question need answers fast?

Question

Describe geometrically the set of points (x,y,z) in 3 dimensions where
a)y=2,z=3 (x varies freely)
b)y=x (z varies freely)

Answer 1

a) Here y and z represent a point, but then x varies freely... so your point extends into a line. The line goes through y = 2, z = 3 and then has any value for x, so it is parallel to the x-axis.

b) Again, start with the line y = x. This is a diagonal line through the origin (0,0). However, since z varies freely, this extends to be a plane. It is a diagonal plane through the origin following the line y = x.

Answer 2

a) y = 2, z = 3, x varies ---- a line parallel to x axis (floating at a height of 2 (y) and a depth of 3 (z).

b. y = x , z varies. --- a line 45% (x = y), pointing/slanted into z plane at 45%.

Answer 3

1) y=2, z=3
this is a line in 3D where:
x=a(-infinite y=2,
z=3

2) y=x
this is a plane in 3D where:
y=x
z=b (-infinite
and if you want to solve it as a system the answer is the union of these two plane and line which is:
(x=y,y=2)=>x=2
(y=2)=>y=2
(z=b,z=3)=>z=3

so the union is a point in 3D with the following coordination:
(x,y,z)=(2,2,3)

Answer 4

y=2 is a plane paralel to the xz plan at distance 2
z=3 is a plane paralel to the xy plane al sistance 3
They cut at a straight line paralel to the x axis.(case a)

y=x is the plane though the z axis cutting the xy plane at the line y=x

Answer 5

A is a line - it is free in only one dimension
B is a plane. z and x can vary, y only equals x.

Answer 6

Straight lines

Answer 7

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Answer 8

Think of the x y z cooridate plane. x goes left to right, y goes up and down, z goes into or out of the surface.