The coordinates of the points where the line segment joining `A(5,1,6)` and `B(3,4,1)` crosses the yz-plane are

Options

A. `(0,17/2,13/2)`
B. `(0,-17/2,13/2)`
C. `(0,17/2,-13/2)`
D. `(0,-17/2,-13/2)`

Answer

C

Explanation

Suppose yz-plane divides the line segment segment joining A and B in the ratio `lamda:1`. The coordinates of the point C of division are `((3lamda+5)/(lamda+1),(4lamda+1)/(lamda+1),(lamda+6)/(lamda+1))`.
The point on yz-plane
`:.(3lamda+5)/(lamda+1)=0implieslamda=-5/3`
Hence the coordinates o c are `(0,17/2,-13/2)`