Question

If the coordinates of the point $A,B,C$ and $D$ be $(2,3,-1),(3,5,-3),(1,2,3)$ and $(3,5,7)$ respectively, then the projection of $AB$ on $CD$ is

• A. $0$
• B. $1$
• C. $2$
• D. $\sqrt{3}$

Answer 1

The correct option is A $0$

Given points $A,B,C,D$ are $(2,3,-1),(3,5,-3),(1,2,3),(3,5,7)$ respectively.
Now direction ratio of $AB=\hat{i}+2\hat{j}-2\hat{k}$
and direction ratio of $CD=2\hat{i}+3\hat{j}+4\hat{k}$
Clearly $AB\cdot CD=0$
Hence, projection of $AB$ on $CD$ is $0$.