Physics · Motion In A Plane · NEET
Only if the number is negative. If lambda is positive (like 2 or 0.5), the new vector lambda-A points in the SAME direction as A, just longer or shorter. If lambda is negative (like -1 or -1.5), the new vector points in the OPPOSITE direction. So a positive scalar only scales the length; a negative scalar scales the length AND reverses the arrow.
Two things happen at once. The magnitude becomes |lambda| times the original magnitude (the sign is dropped for length, because length is always positive). The direction becomes exactly opposite. Example: if A points east with magnitude 5, then -2A points west with magnitude 10. This is why -A is called the negative of A: it is A reversed, same length.
Yes. NCERT states clearly that lambda can be a scalar with its own physical dimension. When it has units, the product lambda-A gets NEW units. Example 1: velocity (a vector) multiplied by time (a scalar with unit second) gives displacement, so s = v t. Example 2: force divided by mass, which is multiplying force by the scalar 1/m, gives acceleration, so a = F/m. This is the idea behind almost every NEET formula that turns one vector into another.
Yes. The magnitude of 2A is exactly 2 times the magnitude of A, and it points the same way. If A has magnitude 3 m pointing north, then 2A has magnitude 6 m pointing north. Nothing about the direction changes because 2 is positive.
A scalar is just a number with magnitude only (like mass, time, temperature). Scalar multiplication of a vector is the OPERATION of multiplying a vector by such a number. The input is one vector plus one number; the output is always another vector (never a scalar). Do not confuse this with the dot product, which multiplies two vectors and gives a scalar.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
It is an operation where a vector A is multiplied by a scalar (real number) lambda to produce a new vector lambda-A. The result has magnitude |lambda| times |A| and the same direction as A if lambda is positive, or opposite direction if lambda is negative.
It is always a vector. Multiplying a vector by a number scales its length and possibly flips its direction, but the output still has both magnitude and direction, so it remains a vector.
Dividing force F by mass m is the same as multiplying the force vector by the scalar 1/m. Since 1/m is positive, acceleration a points in the same direction as the net force, and its size is |F| divided by m. This is a direct NEET use of scalar multiplication.
If you multiply a unit vector n-hat (magnitude 1) by a scalar A, you get a vector of magnitude |A| pointing along n-hat. This is exactly how any vector is written as magnitude times unit vector, for example the components Ax i and Ay j.
Almost every physics formula that converts one vector into another uses scalar multiplication: displacement = velocity times time, momentum = mass times velocity, force = mass times acceleration. Understanding that the scalar only stretches or flips the arrow helps you predict directions correctly in mechanics and electromagnetism questions.
