Question

Let `vec n` be a vector of magnitude `2 sqrt3` such that it makes equal acute angle with the coordinate axes. Find the vector and cartesian forms of the equation of plane passing from ( 1 , -1 , 2) and normal to `vec n`.

Answer 1

`D_r=(cosalpha,cosalpha,cosalpha)`
`=l^2+m^2+n^2=1`
`=3cos^2alpha=1`
`cosalpha=pm1/sqrt3`
`cosalpha=1/sqrt3`
`vecn=2sqrt3(cosalphahati+cosbetahatj+cosgammahatk)`
`=2hati+2hatj+2hatk`
`[vecr-(hati-hatj+2hatk)]*[2hati+2hatj+2hatk]=0`
`[(x-1)hati+(y+1)hatj+(z-2)hatk][2hati+2hatj+2hatk]=0`
`2(x-1)+2(y+1)+2(z-2)=0`
`x+y+z=2`.