Q. 33.7( 3 Votes )

Find the vector equation of the coordinates planes.

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



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