Question

The length of the perpendicular drawn from `(1,2,3)` to the line `(x-6)/3=(y-7)/2=(z-7)/(-2)` is a. `4` b. `5` c. `6` d. `7`
A. 4
B. 5
C. 6
D. 7

Answer 1

Correct Answer - d
Let P be the point (1,2,3) and PN be the length of the perpendicular from P on the given line.
Coordinates of point N are `(3lamda+6,2lamda+7,-2lamda+7)`.
Now PN is perpendicular to the given line of vector
`3veci+2vecj-2veck`. Thus,
`3(3lamda+6-1)+2(2lamda+7-2)-2(-2lamda+7-3)=0orlamda=-1`
Then, point N is (3,5,9)
`impliesPN=7`