Statement 1: There exist two points on the `(x-1)/1=y/(-1)=(z+2)/2` which are at a distance of 2 units from point `(1,2,-4)dot` Statement 2: Perpendicular distance of point `(1,2,-4)` form the line `(x-1)/1=y/(-1)=(z+2)/2` is 1 unit.

Options

A. Both the statements are true, and Statement 2 is the correct explanation for Statement 1.
B. Both the Statements are true, but Statement 2 is not the correct explanation for Statement 1.
C. Statement 1 is true and Statement 2 is false.
D. Statement 1 is false and Statement 2 is true.

Answer

b

Explanation

Any point on the line `(x-1)/(1) = (y)/(-1)= (z+2)/(2)` is
`" "B(t+1, -t, 2t-2), t in R`.
Also, AB is perpendicular to the line, where A is `(1, 2, -4)`. Thus,
`" "1(t)-(-t-2)+ 2(2t+2)=0`
or `" "6t+6=0`
or `" "t=-1`
Point B is `(0, 1, -4)`
Hence, `AB= sqrt(1+1+0)=sqrt2`