The equation of the plane which passes through the point of intersection of lines `""(x-1)/3=(y-2)/1=(z-3)/2"","and"(x-3)/1=(y-1)/2=(z-2)/3` and at greatest distance from point `(0,0,0)` is a. `4x+3y+5z=25` b. `4x+3y=5z=50` c. `3x+4y+5z=49` d. `x+7y-5z=2`

Options

A. `4x+3y+5z=25`
B. `4x+3y+5z=50`
C. `3x+4y+5z=49`
D. `x+7y+5z=2`

Answer

b

Explanation

Let a point `(3lamda+1,lamda+2,2lamda+3)` of the first line also lies on the second line. Then
`(3lamda+1-3)/(1)=(lamda+2-1)/(2)=(2lamda+3-2)/(3)orlamda=1`
Hence, the point of intersection P of the two lines is (4,3,5)
Equation of plane perpendicular to OP, where O is (0,0,0), and passing through P is `4x+3y+5z=50`.