The positon vector of a particle is r⃗-a⌊cosωt î |sinωt ĵ]. The velocity of the particle is (a)

step 1 Hello students here we have a question. The position vector of a particle is R is equal to a cau

The positon vector of a particle is r⃗-a⌊cosωt î |sinωt ĵ]....

The positon vector of a particle is $\vec{r}-a\lfloor\cos \omega t \hat{i} \mid \sin \omega t \hat{j}]$. The velocity of the particle is
(a) parallcl to position voctor
(b) dirceted towards origin
(c) dirceled away from origin
(d) perpendicular to position vector.

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Key Concepts

Perpendicular Vectors

Two vectors are perpendicular if their dot product equals zero. In the context of circular motion, the velocity vector being tangent to the circle ensures that it is orthogonal (perpendicular) to the radial position vector, pointing directly towards or away from the center.

Position and Velocity Vectors

These vectors describe the location and instantaneous motion of a particle. The position vector points from a reference point (often the origin) to the particle’s location, while the velocity vector represents the rate and direction of the particle’s change in position with respect to time.

Circular Motion

This is a type of motion where a particle moves along a circular path. In uniform circular motion, the magnitude of the position vector (radius) remains constant, and the velocity vector, always tangent to the circle, is perpendicular to the position vector.

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