Question

 Write the equation of the plane 3x + 4y -2z = 5 in the vector form.

Answer 1

 The equation of the given plane is 3x+ 4y-2z = 5
Let `bar "r" = "x"hat"i" +"y"hat"j" + "z"hat"k"` be any vector in the plane and 3 , 4 ,-2 are direction ratios of `bar"n"` , which is normal to the plane
` therefore bar"n" = 3hat"i" +4hat"j" -2hat"k"`
`therefore ("x"hat"i" +"y"hat"j" +"z"hat"k") . (3hat"i" +4hat"j" -2hat"k") = 5`
`therefore bar"r" . (3hat"i" +4hat"j" -2hat"k") = 5` which is required form.