Final answer:
To find the perpendicular distance from the origin to the line joining the points (cosθ, sinθ) and (cosϕ, sinϕ), we can use the concept of dot product. The dot product of a vector with a unit vector in the direction perpendicular to the line gives the perpendicular distance.
Step-by-step explanation:
In order to find the perpendicular distance from the origin to the line joining the points (cosθ, sinθ) and (cosϕ, sinϕ), we can use the concept of dot product. The dot product of a vector with a unit vector in the direction perpendicular to the line gives the perpendicular distance.
Let's consider the vector joining the two points, V = (cosϕ - cosθ, sinϕ - sinθ). The unit vector perpendicular to this line is given by U = (-sinϕ + sinθ, cosϕ - cosθ). The dot product of V and U gives us the perpendicular distance from the origin.
The dot product D = V • U = (cosϕ - cosθ)(-sinϕ + sinθ) + (sinϕ - sinθ)(cosϕ - cosθ).