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    • Vector Quantity
    • Scalar Quantity
    • Representation of A Vector
    • Modulus/Magnitude of A Vector
    • Types of Vector
    • Composition of Vectors
    • Triangle Law of Vector Addition
    • Parallelogram Law of Vector Addition
    • Polygon Law of Vector Addition
    • Resolution of A Vector

    A physical quantity which has both magnitude and direction and obeys the rules of vector algebra is known as vector or vector quantity. It is denoted by alphabetical letter(s) with an arrow- head over it. Electric currentand pressure have both magnitude and direction but they do not obey the rules of vector algebra. So, electric current and pressur...

    A physical quantity which has magnitude only but no direction is called a scalar quantity. Scalar quantity obeys the rules of simple algebra (scalar algebra). It is denoted by an alphabetical letter. For Example:mass, length, time, distance, speed etc.

    Any vector ($\overrightarrow{a}$) can be expressed as $\overrightarrow{a}$ = a1$\widehat{i}$ + a2$\widehat{j}$ + a3$\widehat{k}$ Where a1, a2 and a3are components of $\overrightarrow{a}$ along X, Y and Z-axis respectively and $\widehat{i}$, $\widehat{j}$ and $\widehat{k}$ are unit vectors along X, Y and Z-axis respectively.

    The modulus of any vector $\overrightarrow{a}$ = x$\widehat{i}$ + y$\widehat{j}$ + z$\widehat{k}$ is denoted by $\left| \overrightarrow{a} \right|$ and given by: $\left| \overrightarrow{a} \right|$ = $\sqrt{{{x}^{2}}+{{y}^{2}}+{{z}^{2}}}$ unit. Q. Find the magnitude (modulus) of given vector $\overrightarrow{a}$ = 3$\widehat{i}$ – 2$\widehat{j}$ + ...

    1. Unit vector:

    A vector which has magnitude one (unity) is called unit vector. It is denoted by an alphabetical letter with the cap over it. Example: $\widehat{a}$, $\widehat{b}$, $\widehat{i}$, $\widehat{j}$ ,$\widehat{k}$ etc. Mathematically, the unit vector along a vector, $\overrightarrow{a}$ is given by $\widehat{a}$ = $\frac{\overrightarrow{a}}{\left| \overrightarrow{a} \right|}$ $\widehat{i}$, $\widehat{j}$ and $\widehat{k}$ are the unit vectors along x, y and z – axis respectively. Q. Find the unit...

    2. Null vector:

    A vector which has magnitude zero is called null vector. This vector is generally used to indicate the direction of physical quantity. i.e $\overrightarrow{a}$ is null vector if $\left| \overrightarrow{a} \right|$ = 0

    3. Parallel vector:

    Two vectors of the same or different magnitude are said to be parallel vectors if they act in the same direction. In figure, $\overrightarrow{A}$ and $\overrightarrow{B}$ are parallel vectors.

    The process of obtaining a single vector from two or more vectors is called the composition of vectors. The single vector obtained as a result is called the resultant vector.

    Statement:When two vectors acting simultaneously at a point be represented by two sides of a triangle taken in same order both in magnitude and direction then the third side taken in reverse order represents their resultant both in magnitude and direction. Proof: Let us consider two vectors acting simultaneously at a point be represented by two sid...

    Statement:When two vectors acting simultaneously at a point be represented by two adjacent sides of a parallelogram starting from the same point both in magnitude and direction then the diagonal starting from the same point represents their resultant both in magnitude and direction. Proof: Let us consider two vectors $\overrightarrow{P}$ and $\over...

    It states that when a number of vector acting simultaneously at a point be represented by different sides of a polygon taken in same order both in magnitude and direction then, the closing side of polygon taken in reverse order represents the resultant both in magnitude and direction. Let us consider five vectors $\overrightarrow{A}$, $\overrightar...

    The process of splitting a vector into its constituent components is called resolution of a vector. If resolution of a vector is carried out in such a way that the two components are perpendicular to each other then the components are known as rectangular components of the vector. Let the vector $\overrightarrow{A}$ be represented by the side OA bo...

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