For the line `(x-1)/1=(y-2)/2=(z-3)/3,` which one of the following is correct? a. it lies in the plane `x-2y+z=0` b. it is same as line `x/1=y/2=z/3` c. it passes through `(2,3,5)` d. it is parallel t the plane`x-2y+z-6=0`

Options

A. It lies in the plane `x-2y+z=0`
B. It is same as line `(x)/(1)=(y)/(2)=(z)/(3)`
C. It passes through (2,3,5)
D. It is parallel to the plane `x-2y+z-6=0`

Answer

c

Explanation

(1,2,3) satisfies the plane `x-2y+z=0` and also
`(hati+2hatj+3hatk).(hati-2hatj+hatk)=0`
Since the lines `(x-1)/(1)=(y-2)/(2)=(z-3)/(3)and(x)/(1)=(y)/(2)=(z)/(3)`
both satisft (0,0,0) and (1,2,3) both are same. Given line is obviously parallel ot the plane `x-2y+z=6`.