Physics · Motion In A Plane · NEET
Yes. NCERT states it plainly: the two vectors are arranged head to tail, so it is called the head-to-tail method, and since the two vectors and their resultant form three sides of a triangle, it is also called the triangle method of vector addition. Same procedure, two names.
Head to TAIL. Place the tail (start) of the second vector exactly on the head (arrow tip) of the first vector. If you accidentally join head to head or tail to tail, you are no longer using the triangle law and you will get the wrong direction. Only after correct head-to-tail placement do you draw the resultant.
R = A + B (just adding numbers) is true ONLY when the two vectors point in the same direction (angle = 0). In general the vectors point at an angle theta, so the resultant magnitude is R = sqrt(A^2 + B^2 + 2AB cos theta). Vectors have direction, so you add them geometrically (close the triangle), not like plain numbers.
The resultant is the CLOSING side - the one drawn from the tail of the first vector to the head of the second vector. Important: its arrow points from start to finish. The two original vectors go head-to-tail (same sense around the triangle); the resultant goes the opposite sense, joining the free ends.
No. NCERT shows that finding B + A gives the same resultant R as A + B. Vector addition is commutative: A + B = B + A. The triangle just tilts the other way, but the closing side (resultant) has the same magnitude and direction.
They give the SAME resultant; they are just two drawings of one rule. In the triangle law you place vectors head-to-tail and the resultant is the closing side. In the parallelogram law you bring both tails to a common point, complete a parallelogram, and the diagonal from that common point is the resultant. Use triangle law when adding many vectors in a chain; use parallelogram law when two vectors act from the same point.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
If two vectors are represented in magnitude and direction by the two sides of a triangle taken in order (head to tail), then their resultant is represented in magnitude and direction by the third side of the triangle taken in the opposite order (from the tail of the first to the head of the second).
R = sqrt(A^2 + B^2 + 2AB cos theta), where theta is the angle between the two vectors when their tails are together. The direction is given by tan(alpha) = (B sin theta) / (A + B cos theta), where alpha is the angle the resultant makes with vector A.
If three vectors are drawn head-to-tail and form a closed triangle (the head of the last meets the tail of the first), their vector sum is zero. This is why three forces represented by the sides of a triangle taken in order add to zero - a common NEET result.
Yes. Keep placing each new vector head-to-tail after the previous one (this becomes the polygon law). The resultant is the single vector from the tail of the very first vector to the head of the very last vector.
Motion in a plane, projectile motion, relative velocity (rain-man, river-boat) and force problems all require adding vectors. The triangle law is the base rule; the resultant formula R = sqrt(A^2 + B^2 + 2AB cos theta) appears directly in many single-line MCQs.
