There is a set of parallel lines in the scene. How would i Compute mathematically their vanishing point on the image plane.  The 3D line is represented by the set of points [x(t), y(t), z(t)] T, where x(t)=A1+B1(t), y(t)=A2+B2(t), z(t)=A3+B3(t) (t is a range from negative infinity to infinity). The 3D point [A1, A2, A3] T is one point on the line, and the 3D vector [B1, B2, B3]T is the orientation of the line.]

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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There is a set of parallel lines in the scene. How would i Compute mathematically their vanishing point on the image plane. 

The 3D line is represented by the set of points [x(t), y(t), z(t)] T, where x(t)=A1+B1(t), y(t)=A2+B2(t), z(t)=A3+B3(t) (t is a range from negative infinity to infinity).
The 3D point [A1, A2, A3] T is one point on the line, and the 3D vector [B1, B2, B3]T is the orientation of the line.]

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