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% Document Info
\author{rehman225}
\pdfinfo{
  /Title (physics-elements-of-vectors.pdf)
  /Creator (Cheatography)
  /Author (rehman225)
  /Subject (Physics - Elements of vectors Cheat Sheet)
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        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Physics - Elements of vectors Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{rehman225} via \textcolor{DarkBackground}{\uline{cheatography.com/152970/cs/33046/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}rehman225 \\
  \uline{cheatography.com/rehman225} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 7th July, 2022.\\
   Updated 7th July, 2022.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{multicols*}{2}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Scalar}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{Physical quantities having only magnitude but not associated with any direction are called scalar quantities.} \tn 
% Row Count 3 (+ 3)
% Row 1
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\mymulticolumn{1}{x{8.4cm}}{scalars are added and subtracted by algebraic method.} \tn 
% Row Count 5 (+ 2)
% Row 2
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\mymulticolumn{1}{x{8.4cm}}{{\bf{Ex}} : Mass, speed work, power, energy, pressure etc.} \tn 
% Row Count 7 (+ 2)
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\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Graphical representation of a Vector}}  \tn
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\mymulticolumn{1}{p{8.4cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/rehman225_1657149038_832bbda747525b4970ddc92fc65e5c24.png}}} \tn 
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\mymulticolumn{1}{x{8.4cm}}{A vector can be represented graphically by a directed line segment. The length of the line segment is magnitude of the vector and the arrow head represents the direction of vector.}  \tn 
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\par\addvspace{1.3em}

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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Triangle law of vectors}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{The famous triangle law can be used for the addition of vectors and this method is also called the head-to-tail method.} \tn 
% Row Count 3 (+ 3)
% Row 1
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\mymulticolumn{1}{x{8.4cm}}{As per this law, two vectors can be added together by placing them together in such a way that the first vector's head joins the tail of the second vector.} \tn 
% Row Count 7 (+ 4)
% Row 2
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\mymulticolumn{1}{x{8.4cm}}{Thus, by joining the first vector's tail to the head of the second vector, we can obtain the resultant vector sum.} \tn 
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Scalar Product/Dot Product of Vectors}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{The resultant of scalar product/dot product of two vectors is always a scalar quantity.} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{8.4cm}}{Consider two vectors a and b.The scalar product is calculated as the product of magnitudes of a, b, and cosine of the angle between these vectors.} \tn 
% Row Count 5 (+ 3)
% Row 2
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\mymulticolumn{1}{x{8.4cm}}{{\bf{Scalar product = |a||b| cos α}}} \tn 
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% Row 3
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\mymulticolumn{1}{x{8.4cm}}{Here, |a| = magnitude of vector a, |b| = magnitude of vector b, α = angle between the vectors} \tn 
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Vector}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{Physical quantities having both magnitude and direction are called as vector quantities.} \tn 
% Row Count 2 (+ 2)
% Row 1
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\mymulticolumn{1}{x{8.4cm}}{{\bf{Ex}} : Displacement, Velocity, acceleration, force, momentum etc.} \tn 
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Types of vectors}}  \tn
% Row 0
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{\bf{Null Vector}} & It is a vector whose magnitude is zero and direction is not specified \tn 
% Row Count 3 (+ 3)
% Row 1
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{\bf{Equal Vector}} & Two vectors are said to be equal if they have same magnitude and direction irrespective of their initial points \tn 
% Row Count 8 (+ 5)
% Row 2
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{\bf{Negative Vector}} & A vector with same magnitude but opposite in direction is called negative vector \tn 
% Row Count 12 (+ 4)
% Row 3
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{\bf{Unit Vector}} & A vector whose magnitude is unity is termed as unit vector \tn 
% Row Count 15 (+ 3)
% Row 4
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{\bf{Parallel Vector}} & If two vectors are in same direction then they are said to be parallel or like vectors. \tn 
% Row Count 19 (+ 4)
% Row 5
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{\bf{Position vectors}} & The vector which is used to specify the position of a point 'p' with respect to some fixed point 'o' represented by OP is known as position vector of 'p' with respect to 'o'. \tn 
% Row Count 26 (+ 7)
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Parallelogram Law of Addition of Vectors}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{Another law that can be used for the addition of vectors is the parallelogram law of the addition of vectors.} \tn 
% Row Count 3 (+ 3)
% Row 1
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\mymulticolumn{1}{x{8.4cm}}{Let's take two vectors p and q, as shown below. They form the two adjacent sides of a parallelogram in their magnitude and direction.} \tn 
% Row Count 6 (+ 3)
% Row 2
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\mymulticolumn{1}{x{8.4cm}}{The sum p + q is represented in magnitude and direction by the diagonal of the parallelogram through their common point.} \tn 
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\begin{tabularx}{8.4cm}{X}
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\mymulticolumn{1}{x{8.4cm}}{\bf\textcolor{white}{Cross Product}}  \tn
% Row 0
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\mymulticolumn{1}{x{8.4cm}}{If the product of two vectors is another vector then such a product is called vector product or cross product.} \tn 
% Row Count 3 (+ 3)
% Row 1
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\mymulticolumn{1}{x{8.4cm}}{If θ is the angle between the given two vectors A and B, then the formula for the cross product of vectors is given by:} \tn 
% Row Count 6 (+ 3)
% Row 2
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\mymulticolumn{1}{x{8.4cm}}{{\bf{A × B = |A| |B| sin θ}}} \tn 
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% That's all folks
\end{multicols*}

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