Find the Cartesian equation of the following plane:
r.(2^i+3^j−4^k)=1
Given vector equation is r.(2^i+3^j−4^k)=1 ...(ii)
for any arbitrary point P(x,y,z) on the plane , position vector r is given by x^i+y^j+z^k
Substituting the value of r in Eq. (ii), we obtain
(x^i+y^j+z^k).(2^i+3^j−4^k)=1⇒2x+3y−4z=1
which is the required Cartesian form.