Find the vector equation of the coordinates planes.

Question

Philoid · Accepted Answer

Here we need to find the vector equation of the xy-plane, xz-plane and yz-plane.

For xy-plane

We know the xy-plane passes through the point i.e., origin and is perpendicular to the z-axis, so

Let and …….(i)

We know that, vector equation of a plane passing through a point and normal to is given by

Substituting the values from equation (i), we get

(by multiplying the two vectors using the formula )

For xz-plane

We know the xz-plane passes through the point i.e., origin and is perpendicular to the y-axis, so

Let and …….(iii)

We know that, vector equation of a plane passing through a point and normal to is given by

Substituting the values from equation (iii), we get

(by multiplying the two vectors using the formula )

For yz-plane

We know the yz-plane passes through the point i.e., origin and is perpendicular to the x-axis, so

Let and …….(v)

We know that, vector equation of a plane passing through a point and normal to is given by

Substituting the values from equation (v), we get

(by multiplying the two vectors using the formula )

Hence from equation (ii), (iv) and (vi), we get

The equation of xy, yz and yz plane as