Find the equation of the perpendicular from point `(3,-1,11)` to line `x/2=(y-2)/3=(z-3)/4`. Also, find the coordinates of foot of perpendicular and the length of perpendicular.

Options

A. `sqrt47 ` units
B. 7 units
C. `sqrt53` units
D. 8 units

Answer

C

Explanation

Now `x_2-x_1=-1`
`x_2-3=-1`
`:. X_2=1`
Similarly,
`y_2-y_1=6`n
`y_2+1=6`
`:. Y_2=5`
`and z_2-z_1=-4`
`z_2-11=-4`
`z_2=-4+11=7`
`:." Co-ordinate of Q is (2,5,7)`
`:." Length of segment PQ"`
`=sqrt((2-3)^2+(5++1)^2+(7-11)^2)`
`=sqrt(1+36+16)=sqrt53`units.