Let −−→AB=3^i–^j+^k and −−→CD=3^i+2^j+4^k are two vectors. The position vectors of the points →A and →C are 6^i+7^j+4^k and –9^j+2^k, respectively. Find the position vector of a point P on the line AB and a point Q on the line CD such that −−→PQ is perpendicular to the vectors −−→AB and −−→CD.

Let −−→AB=3^i–^j+^k and −−→CD=3^i+2^j+4^k are two vector

1.	Let −−→AB=3^i–^j+^k and −−→CD=3^i+2^j+4^k are two vectors. The position vectors of the points →A and →C are 6^i+7^j+4^k and –9^j+2^k, respectively. Find the position vector of a point P on the line AB and a point Q on the line CD such that −−→PQ is perpendicular to the vectors −−→AB and −−→CD.
Answer» Let $- - \to A B = 3^i -^j +^k$ and $- - \to C D = 3^i + 2^j + 4^k$ are two vectors. The position vectors of the points $\to A$ and $\to C$ are $6^i + 7^j + 4^k$ and $- 9^j + 2^k$ , respectively. Find the position vector of a point $P$ on the line $A B$ and a point $Q$ on the line $C D$ such that $- - \to P Q$ is perpendicular to the vectors $- - \to A B$ and $- - \to C D$ .