Shortest Distance Between Two Lines in 3D Space, Solved Examples | Class 12 Math Notes Study Material Download Free PDF

The shortest distance between two lines in three-dimensional space is the length of the perpendicular segment drawn from a point ...
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Angles Between two Lines in 3D Space: Solved Examples | Class 12 Math Notes Study Material Download Free PDF

A line in mathematics and geometry is a fundamental concept representing a straight, one-dimensional figure that extends infinitely in both ...
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Equation of Line in Three Dimensions | Cartesian & vector Equation | Class 12 Math Notes Study Material Download Free PDF

Equation of a line is defined as y= mx+c, where c is the y-intercept and m is the slope. Vectors ...
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Direction Cosines & Direction Ratios – Definitions & Examples | Class 12 Math Notes Study Material Download Free PDF

Direction Cosines When a directed line OP passing through the origin makes \(\begin{array}{l}\alpha \end{array} \) , \(\begin{array}{l}\beta\end{array} \) and \(\begin{array}{l} ...
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Scalar or Dot Product Of Two Vectors | Projection of Vector | Definition, Properties, Formulas and Examples | Class 12 Math Notes Study Material Download Free PDF

Vector is a quantity that has both magnitude and direction. Some mathematical operations can be performed on vectors such as ...
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Multiplication Of Vectors by a Scalar Quantity with examples | Class 12 Math Notes Study Material Download Free PDF

A vector relates two given points. It is a mathematical quantity having both the Magnitude and the direction. Multiplication of ...
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Laws of Vector Addition- Parallelogram, Triangle Law, Vector Addition | Class 12 Math Notes Study Material Download Free PDF

Laws of Vector Addition A vector is a physical quantity which is represented both in direction and magnitude. In the ...
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Types of Vectors | Zero Vector, Unit Vector, Position Vector, Co-initial Vector, Like & Unlike Vectors, Co-planar Vectors, Collinear Vectors, Equal Vectors, Displacement Vector, Negative of a Vector

What is a vector? Vector is a physical quantity that has both direction and magnitude. In other words, the vectors ...
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Vectors in Maths-Unit Vector, Zero or null Vector, Magnitude of Vector, Operations on Vectors, Dot product of  Vectors, Scalar Triple Product

Vectors, in Maths, are objects which have both, magnitude and direction. Magnitude defines the size of the vector. It is represented ...
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Separable Differential Equation-Solved Examples | Class 12 Math Notes Study Material Download Free PDF

A differential equation is an equation of the form \(\begin{array}{l}\frac{\mathrm{d} y}{\mathrm{d} x} = g(x),\;\;\;\; where\;\; y = f(x)\end{array} \). General ...
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