**Vector Operations: **The vectors can be added, subtracted or
multiplied with one another. Addition of vectors, difference of vectors, multiplication
of a vector by a scalar, product of vectors, etc. are called **vector operations**.

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**Addition of Vectors**

Study the following three cases:

**Case I:**

**Case II:**

**Case III:**

**Triangle Law of Vector Addition**

**Definition:**

The triangle law of vector addition states that:
“** If the magnitude and direction of two vectors are represented by two sides of
a triangle taken in order, then the magnitude and direction of their sum is
given by the third side taken in reverse order.**”

**Parallelogram Law of Vector Addition**

**Definition:**

The parallelogram law of vector addition states
that: “** If two adjacent sides of a parallelogram through a point represents two
vectors in magnitude and direction, then their sum is given by the diagonal of
the parallelogram through the same point in magnitude and direction.**”

**Polygon Law of Vector Addition**

**Definition:**

The polygon law of vector addition states that:
“** If a number of vectors can be represented in magnitude and direction by the
sides of polygon taken in order, their sum is given in magnitude and direction
by the closing side of the polygon taken in reverse order.**”

**Addition of Two Vectors in Components Form**

**Geometrical Proof:**

**Subtraction of Vectors**

**Multiplication of a Vector by a Scalar**

**Unit Vectors i And j**

**Worked Out Examples**

*Do you have any
questions regarding the vector operations?*

*Do you have any questions regarding the vector operations?*

*You can ask your questions or problems here, in
the comment section below.*

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