Question

 Find the equation of the lines passing through the point (2, 1, 3) and perpendicular to the lines

Answer 1

 Passing through point (2, 1, 3)        .........given
(x, y, z) = (2, 1, 3)
 Perpendicular to the lines. 
`(x-1)/1 = (y-2)/2 =(z-3)/3`  and `X/-3 = Y/2 = Z/5`

Let `veca = hati +2hatj + 3k`
`barb = -3hatj + 2hatj + 3k`

`baraxxhatb = |(hati   hatj   hatk),(1   2   3),(-3  2  5)|`
            `=hati(10-6)-j(5+9)+hatk(2+6)`
            `= 4hati - 14hatj + 8k`

D.r.’s of required line :   4, - 14,8
                                     i.e, 2,-7,4

Required equation of line `(x-2)/2 = (y-1)/-7 = (z - 3)/4`