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. $AB\mathrm{ta}n\theta$
• D. $CD\cos \theta$

Answer 1

The correct option is B

$AB\cos \theta$

Explanation for the correct answer:

Consider the figure

Let $EB$ be the perpendicular from the point $B$ to the line $CD$.

A right-angled triangle $△AEB$ is thus formed.

As the angle between lines $AB$ and $CD$ is $\theta$.

So, $\angle BAE=\theta$

The projection of the segment $AB$ on line $CD$ is segment $AE$.

In $△AEB$,

$\frac{AE}{AB}=\cos \theta$

$\Rightarrow$$AE=AB\cos \theta$
Hence, the projection of segment $AB$ on line $CD$ is $AB\cos \theta$.

Thus, option(B) is the correct answer.