Physics · Motion In A Plane · NEET
Four steps. (1) Resolve each vector: for a vector A at angle theta, Ax = A cos(theta) and Ay = A sin(theta). (2) Add all x-components: Rx = Ax + Bx. (3) Add all y-components: Ry = Ay + By. (4) Combine: magnitude R = sqrt(Rx^2 + Ry^2) and direction tan(theta) = Ry / Rx. Example: A = 3 along +x, B = 4 along +y gives Rx = 3, Ry = 4, so R = sqrt(9 + 16) = 5 at tan(theta) = 4/3 above the x-axis.
Because vectors have direction. Adding magnitudes (3 + 4 = 7) only works if both vectors point the same way. When they point in different directions, part of each vector cancels or adds along each axis. Resolving into components lets you add same-direction parts (all x together, all y together) correctly. That is why 3 and 4 at right angles give 5, not 7.
They give the same answer; they are just different tools. The parallelogram law uses one formula R = sqrt(A^2 + B^2 + 2AB cos(theta)) with the angle between the two vectors. The analytical method resolves each vector into x and y components and adds them separately. The component method is easier when you have three or more vectors, or when angles are messy, because you never need the angle between the vectors directly.
By default the angle from tan(theta) = Ry / Rx is measured from the positive x-axis (anticlockwise). Always check the signs of Rx and Ry to place the resultant in the correct quadrant. In force problems the direction is often quoted 'with respect to' one of the given forces, so read the question — the same resultant can be reported as an angle from the 8 N force or from the 6 N force.
Rx is the total x-component (sum of all x-parts) and Ry is the total y-component (sum of all y-parts) of the resultant. The magnitude is R = sqrt(Rx^2 + Ry^2). The angle with the x-axis is theta = tan inverse (Ry / Rx). If Rx = 8 and Ry = 6, then R = 10 and theta = tan inverse (6/8) = tan inverse (3/4).
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.
It is a method that resolves each vector into perpendicular x and y components, adds the x-components to get Rx and the y-components to get Ry, then finds the resultant as R = sqrt(Rx^2 + Ry^2) with direction tan(theta) = Ry / Rx.
R = sqrt(Rx^2 + Ry^2), where Rx is the sum of all x-components and Ry is the sum of all y-components. The angle with the x-axis is theta = tan inverse (Ry / Rx).
When they are perpendicular. Then one force is the whole Rx and the other is the whole Ry, so R = sqrt(F1^2 + F2^2) directly, as in the 8 N and 6 N NEET problem giving 10 N.
Both give the same resultant. The parallelogram law uses the angle between the two vectors in one formula; the analytical method splits every vector into components and is better for three or more vectors.
Projectile motion, forces, and relative velocity in a plane all use x and y components. Mastering resolve-then-add lets you solve these fast without drawing parallelograms in the exam.
