Question

If a line segment of length “l” makes an angle $\theta$ with a line then the projection of the line segment on the line will be -

• A.
• B.
• C.
• D.

Answer 1

The correct option is B


Let a & b be two vectors. So, a & b are their respective magnitudes.
We’ll form a triangle by dropping a perpendicular from a to b. We can see that the so formed triangle is a right angle triangle.
As the angle between a & b is $\theta$ so we can write -
$Cos\left(\theta \right)=\frac{base}{hypotenuse}$
Or,$Cos\left(\theta \right)=\frac{base}{\alpha }$
Or base =a $cos\left(\theta \right)$
Here, this base is nothing but the projection of a on b.
Instead of this vector a, in the question we are given a line segment of length “l”. So the projection of this line segment on another line with which it makes an angle $\theta$ will be l $cos\left(\theta \right)$