Shortest distance between line `2x+3y+4z-4=0=x+y+2z-3` and z-axis is -

Options

A. 1
B. 2
C. 4
D. 3

Answer

B

Explanation

We have `x+y+2z-3=0`
and `2x+3y+4z-4=0`
Let a,b,c be the direction ratios of the line, then line lies on the both planes.
`therefore a+b+2c=0 and 2a+3b+4c=0`
On solving these equations by cross-multiplication method.
`a/(4-6)=(b)/(4-4)=(c)/(3-2) Rightarrow (a)/(-2)=(b)/(0)=c/1`
`therefore` Direction ratios of the line is (-2,0,1) and direction ratios of Z-axis (0,0,1)
Hence, distance between Z-axis to the given line is `sqrt((-2-0)(2)+(0)^(2)+(1-1)^(2))=sqrt4=2`