(i) Find the distance of the point (-1,-5,-10) from the point of intersection of the line `vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk)` and the plane `vec(r).(hati - hatj + hatk) = 5.`
(ii) Find the distance of the point with position vector
`- hati - 5 hatj - 10 hatk ` from the point of intersection of the line `vec(r) = (2 hati - hatj + 2 hatk ) + lambda (3 hati + 4 hatj + 12 hatk )` and the plane `vec(r). (hati - hatj + hatk)= 5.`
(iii) Find the distance of the point (2,12, 5) from the point of intersection of the line .
`vec(r) = 2 hati - 4 hatj + 2 hatk + lambda (3 hati + 4 hatj + 12 hatk )`
and the plane `vec(r). (hati - 2 hatj + hatk ) = 0. `

Answer

(i)-(ii) unit (iii) 13 unit.