The distance of the point P(1,2,3) from the line which passes through the point (4,2,2) and parallel to the vector `2hati+3hatj+6hatk` is

Options

A. `sqrt10`
B. `sqrt7`
C. `sqrt5`
D. 1

Answer

A

Explanation

The equation of the of line which passess through the point `A (4,2,2)` and parallel to the vector `2hati + 3hatj + 6hatk` is
`(x-4)/(2) = (y -2)/(3) = (x-2)/(6)`
Distance of point `P(1,2,3)` form the line
`sqrt((1-4)^(2) +(2-2)^(2) (3-2)^(2) - {2(1-4)+3(2-2) +6(3-2)^(2)})`
` = sqrt(9+0+1-(-6 + 0 + 6)^(2)) = sqrt(10)`