Addition and Subtraction of Vectors – Class 11 | Chapter – 4 | Physics Short Notes Series PDF for NEET & JEE

Addition and Subtraction of Vectors: In physics, vectors are used to represent physical quantities that have both magnitude and direction, such as velocity, force, and displacement. Vector addition and subtraction are important operations in physics, as they allow us to combine and analyze these quantities.

Vector addition in physics involves combining two or more vectors to obtain a new vector that represents the combined effect of the original vectors. For example, if an object is moving with a velocity of 5 m/s to the east, and then experiences a force of 10 N to the north, we can find its resulting velocity by adding the velocity vector and the force vector using vector addition.

Vector subtraction in physics involves finding the difference between two vectors. For example, if an object moves from point A to point B, we can find its displacement vector by subtracting the initial position vector (point A) from the final position vector (point B).

Properties of Addition and Subtraction of Vectors

The addition and subtraction of vectors obey several important properties that are essential for solving problems involving vector quantities. Here are some of the key properties:

  • Commutative property: The order of addition or subtraction of vectors does not affect the result. That is, u + v = v + u and uv = -(vu).
  • Associative property: The grouping of vectors does not affect the result. That is, (u + v) + w = u + (v + w) and (uv) – w = u – (v + w).
  • Identity element: There exists a vector 0 such that u + 0 = u and u0 = u for any vector u. The vector 0 is known as the additive identity or zero vector.
  • Inverse element: For any vector u, there exists a vector –u such that u + (-u) = 0 and u – (-u) = u. The vector –u is known as the additive inverse or negative of u.

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