The length of the perpendicular drawn from `(1,2,3)` to the line `(x-6)/3=(y-7)/2=(z-7)/(-2)` is

Options

A. 5 units
B. 7 units
C. 4 units
D. None of these

Answer

B

Explanation

Let L be the foot the perpendicular drawn from the point ` P ( 1, 2 , 3 ) ` to the given line.
Let the co - ordinates of L be
` ( 3 lamda + 6, 2 lamda + 7, - 2lamda + 7 ) " " `…(i)
` therefore ` Direction ratios of the given line are proportional to 3, 2, - 2
Since PL is perpendicular to the given line.
` therefore 3 ( 3 lamda + 5 ) + 2 ( 2 lamda + 5 ) + ( - 2 ) ( - 2 lamda + 4 ) = 0 `
` rArr lamda = - 1 `
Hence, co - oridinates of L are ` ( 3, 5, 9 )
` therefore PL = sqrt ( ( 3 - 1 ) ^ 2 + ( 5 - 2 ) ^ 2 + ( 9 - 3 ) ^ 2 )) = ` 7 units