Physics · Work, Energy And Power · NEET
It is always a scalar, meaning a plain number with no direction. Even though you start with two vectors, A.B = AB cos theta gives you one value like 5 J or 140 W. This is exactly why it is called the scalar product. In NEET, whenever you see a dot between two vectors, expect a number as the final answer.
The name describes the output, not the input. You put in two vectors, but the operation cos theta removes the direction and leaves only a magnitude. So the product of two vectors becomes a scalar. Compare this with the cross product (A x B), which gives a new vector.
Dot product A.B = AB cos theta gives a scalar (number) and uses the cosine of the angle. Cross product A x B = AB sin theta gives a vector and uses the sine of the angle. Simple rule for NEET: dot uses cos and gives a number; cross uses sin and gives an arrow perpendicular to both.
It means you multiply the length of A, the length of B, and cos theta of the angle between them. The cos theta part keeps only the component of one vector along the other. If the two vectors point the same way (theta = 0), cos 0 = 1, so you get the full product AB. If they are perpendicular (theta = 90 degrees), cos 90 = 0, so the dot product is zero.
Multiply matching components and add them. If A = Ax i + Ay j + Az k and B = Bx i + By j + Bz k, then A.B = Ax Bx + Ay By + Az Bz. The i.i, j.j, k.k terms give 1 and all mixed terms like i.j give 0, because the axes are perpendicular. This component method is the fastest way to solve NEET questions.
Yes. When theta is between 90 and 180 degrees, cos theta is negative, so A.B is negative (this gives negative work). When theta = 90 degrees, cos theta = 0, so A.B = 0 even if both vectors are non-zero. A zero dot product is the quick test that two vectors are perpendicular.
A particle moves from a point (-2i + 5j) to (4j + 3k) when a force of (4i + 3j) N is applied. How much work is done by the force?
A particle moves with a velocity (6i - 4j + 3k) m/s under the action of a constant force F = (10i + 10j + 20k) N. The instantaneous power applied to the particle is
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is a way to multiply two vectors that gives a single number. The formula is A.B = AB cos theta, where A and B are the magnitudes and theta is the angle between the vectors.
Work W = F.d = Fd cos theta. Force and displacement are both vectors, but work is a scalar (measured in joules). Only the part of the force along the displacement does work, and cos theta picks out that part.
Yes. The dot product is commutative, so A.B = B.A. Both equal AB cos theta, and the angle between the two vectors is the same either way.
Zero, because the angle is 90 degrees and cos 90 = 0. This is why i.j = j.k = k.i = 0. A zero dot product is the standard test for perpendicular vectors.
It is used directly in work (W = F.d), power (P = F.v), and to find the angle between two vectors. Many NEET Work, Energy and Power questions are solved in one step using component-wise dot products.
