The distance of point `A(-2,3,1)` from the line `P Q` through `P(-3,5,2),` which makes equal angles with the axes is a. `2//sqrt(3)` b. `14//sqrt(3)` c. `16//sqrt(3)` d. `5//sqrt(3)`

Options

A. 2/ `sqrt3`
B. `sqrt(14 //3)`
C. 16/ `sqrt3`
D. 5/ `sqrt3`

Answer

B

Explanation

A(-2 , 3 , 1)

Equation of line PQ
`implies (x+3)/(1) = (y-5)/(1) = (z-2)/(1) = lambda `
`implies Q {{:(x_(1) = x = lambda - 3), (y_(1) = y = lambda + 5), (z_(1) = z = lambda + 2):}}`
AQ `bot` line PQ
`implies {{:(1(lambda - 3 +2)+ 1 (lambda + 5 - 3) + 1 (lambda+2 -1)=0), (3 lambda + 2 = 0 " " implies lambda = (-2)/(3)):}`
AQ = `sqrt(((-11)/(3) +2)^(2) + ((13)/(3) -3)^(2) + ((4)/(3)-1)^(2))`
= `sqrt((25)/(9) + (16)/(9) + (1)/(9))`
= `sqrt((42)/(9)) = sqrt((14)/(3))`