Question

If $\theta$ is the angle between the lines $AB$ and $CD$, then the projection of line segment $AB$ on line $CD$, is:

• A. $AB\sin \theta$
• B. $AB\cos \theta$
• C. $AB\tan \theta$
• D. $CD\cos \theta$

Answer 1

The correct option is B

$AB\cos \theta$

Explanation for the correct option.

Finding the relation:

It is a fundamental concept that, if a vector $\overrightarrow{AB}$, makes an angle $\theta$, with a given line $CD$ in anticlockwise direction, then the projection of $\overrightarrow{AB}$ on $CD$ is a vector $\overrightarrow{p}$with the magnitude $\left|\overrightarrow{AB}\right|\cos \theta$. However, the direction of $\overrightarrow{p}$ depends on the condition that whether $\theta$ is positive or negative.

Hence, option B is correct.