Find the co-ordinates of the foot of perpendicular drawn from point `A(1,6,3)` to the line `(x)/(1) = (y-1)/(2) = (z-2)/(3)`.

Options

A. 3
B. `sqrt11`
C. `sqrt13`
D. 5

Answer

C

Explanation

Given , ` ( x ) / ( 1 ) = ( y - 1 ) /( 2) = ( z - 2 ) /( 3 ) = lamda ` [ say]
Any point on the lines is
` P ( lamda, 2lamda + 1, 3lamda + 2 ) `
Therefore ,direction ratios of PQ are ` lamda - 1, 2lamda - 5, 3 lamda - 1 `
` because P Q ` is perpendicular to the given line.
Therefore
` 1 ( lamda -1 ) + 2 ( 2lamda- 5 ) + 3 ( 3lamda - 1 ) = 0 `
` rArr " " lamda = 1 `
` therefore ` The coordinate of P are ` ( 1, 3, 5 ) `
` therefore ` Length of perpendicular
` = sqrt ( ( 1 - 1 ) ^ 2 + ( 3 - 6 ) ^ 2 + ( 5 - 3 ) ^ 3 ) `
` = sqrt ( 13 ) `