Physics · Motion In A Plane · NEET
Look at which axis the angle touches. The component along the axis from which the angle is measured uses cos; the other component uses sin. If theta is measured from the x-axis, then Ax = A cos theta and Ay = A sin theta. If the angle is given from the y-axis instead, they swap: the x-part becomes A sin theta and the y-part becomes A cos theta. Never memorise blindly - always draw the angle first.
Components let you add or work with vectors using simple arithmetic instead of geometry. Once every vector is written as an x-part and a y-part, you just add all the x-parts and all the y-parts separately. This is the analytical method and it is faster and more exact than drawing triangles, which is why NEET numericals rely on it.
Yes. Ax and Ay are themselves vectors - they have a direction (along x and along y). When we write Ax = A cos theta we usually mean the magnitude of that component. The full vector is A = Ax i + Ay j, where i and j point along x and y.
No. Since cos theta and sin theta are always between 0 and 1 for angles from 0 to 90 degrees, each rectangular component is always less than or equal to the vector's magnitude. The maximum a component can be is A itself, when the vector points exactly along that axis (angle 0).
They are opposite processes. Resolution splits one vector into two perpendicular parts (Ax and Ay). Finding the resultant combines two or more vectors into one. You often resolve first, add the parts, then recombine to get the resultant - both directions use the same cos/sin relations.
The magnitude and direction of the acceleration produced in a body of mass 5 kg when two mutually perpendicular forces 8 N and 6 N act on it are respectively:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
For a vector A at angle theta from the x-axis: Ax = A cos theta (horizontal) and Ay = A sin theta (vertical). To rebuild the vector: magnitude A = sqrt(Ax^2 + Ay^2) and direction theta = tan^-1(Ay / Ax).
Rectangular (or perpendicular) components are the two parts of a vector taken along two perpendicular axes, usually x and y. They are the most useful because they are independent - the x-part does not affect the y-part.
No. Resolution only re-describes the same vector as two perpendicular pieces. When you add Ax and Ay back using the parallelogram (or Pythagoras), you get exactly the original vector.
Almost every 2D problem - projectile motion, forces on an incline, equilibrium, work done - is solved by first resolving vectors into x and y components. Getting cos and sin right here prevents silent mistakes in the whole chapter.
