Question

What restrictions must be made on x, y, and z so that the triple (x, y, z) will represent a point on the y axis? On the z axis? In the xz plane? In the yz plane?

Answer 1

Answer:i) The point on y-axis is (0,y,0)

            ii) The point on z-axis is (0,0,z)

            iii)  The point on x z plane is (x,o,z)

            iv) The point on y z plane is (0,y,z)

Step-by-step explanation:

Explanation:-

i) For every point on x-axis, y-co-ordinate is zero and z- co-ordinate is zero

i .e., y=0 and z=0

The point on x-axis is (x,0,0)

ii) For every point on y-axis, x-co-ordinate is zero and z- co-ordinate is zero

i .e., x=0 and z=0

The point on y-axis is (0,y,0)

iii) For every point on z-axis, x-co-ordinate is zero and y- co-ordinate is zero

i .e., x=0 and y=0

The point on z-axis is (0,0,z)

iv)  For every point on X Z plane then Y=0

The point on x z plane is (x,o,z)

v) For every point on Y Z plane then X=0

The point on yz plane is (0,y,z)

vi) For every point on X Y plane then Z=0

The point on x y plane is (x,y,0)

Answer 2

The point in y-axis are  $(0,y,0)$,  the point at z -axis are, $(0,0,z)$, the point at xz -plane are, $(x,0,z)$ and the point at xz -plane are, $(0,y,z)$.

Given-

i) The point (x, y, z) will represent a point on the y axis -As we know that on the y-axis the other two coordinates will have no point or zero points. Thus at y-axis-

$x=0$

$z=0$

Hence the point at y -axis will be,

$(0,y,0)$

II)  The point  (x, y, z) will represent a point on the z axis -As we know that on the z-axis the other two coordinates will have no point or zero points. Thus at z-axis-

$x=0$

$y=0$

Hence the point at z -axis will be,

$(0,0,z)$

III)  The point (x, y, z) will represent a point  In the xz plane-

In the xz-plane both x and z keeps some value but the y coordinate will be zero in xz plane. Thus In the xz plane-

$y=0$

Hence the point at xz -plane will be,

$(x,0,z)$

iv)The point  (x, y, z) will represent a point  In the yz plane-

In the yz-plane both x and z keeps some value but the y coordinate will be zero in yz plane. Thus In the yz plane-

$x=0$

Hence the point at xz -plane will be,

$(0,y,z)$

Hence, the point in y-axis are  $(0,y,0)$,  the point at z -axis are, $(0,0,z)$, the point at xz -plane are, $(x,0,z)$ and the point at xz -plane are, $(0,y,z)$.

For more about the coordinate plane follow the link below-

https://brainly.com/question/13611766