Find the equation of the plane passing through the point (1, 3, 5) and perpendicular to each of the planes x + 2y + 3z = 7 and 3x + 3y + z = 0, Also find distance of new plane from (2,3,1).

Explanation

`p_1=x+2y+3z=7`
`p_2=3x+3y+z=0`
`n_1=(1,2,3)`
`n_2=(3,3,1)`
since normal vector is also perpendicular
`n2=[[1,j,k],[1,2,3],[3,3,1]] `

on solving,

`n_2=-7hat i +8 hat j_3hat`

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