Vectors Index

Vector product ( Multiplying vectors )

Vector product ( Multiplying vectors )

Vector Product: If we multiply a vector with any other vector or scalar quantity then the result is called vector product.   Multiplying a vector by a scalar: If we multiply a vector by a scalar , then the result is a new vector. The magnitude of the vector formed by multiplying and , is the magnitude of multiplied by and the direction of the vector is same as vector if is positive and exactly oppsite of is negative. And to divide the vector with we can simply multiply the vector with   Multiplying a vector by a...

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Adding vectors by components

Two vector can be easily summed by using vector sum by geometrical method but it is not practical way to add vectors. For a simpler and more practical way of adding two or more vectors then we can use component method of vector sum or add vectors by components.   Let there be three vector , and and if vector is the sum of vectors and or , then, The x component of vector r is the sum of x components of vector a and b , the y component of vector r is the sum of y components of vector a and b and the z component of vector r is the sum...

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Components of vectors

Components of vectors

Components of a vector: The components of a vector are two or more vectors ( Usually vectors along the x , y , z axes) whose vector sum is equal to the given vector. For ease in doing vector calculations Vectors are expressed in the form of two or three components ; Two if the vector is two dimensional and three if the vector is three dimensional . Components of a Two dimensional vector: Consider a two dimensional vector whose initial point is the point “o” the rectangular coordinate system and final point “A”. If we...

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Unit Vector

Unit Vector

Unit Vector: A unit vector is a vector that has a magnitude of exactly 1 unit and points in a particular direction. A unit vector lacks both unit and dimension , But it have a magnitude of a unit and a certain direction. It’s sole purpose is to point toward a direction. A unit vector is denoted by a letter above which a hat (  ) is placed.   The unit vector along any vector ( say vector a ( ) ) is calculated using the formula: Or by dividing the vector by it’s magnitude. Unit Vector along x , y & z axes:   The unit...

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Geometric addition of vectors

Geometric addition of vectors

In physics and mathematics many times we need to add or subtract Vectors. Although there are many ways of combining vectors or adding and subtracting vectors , The simplest and most straight forward method of combining vectors is by graphical method or geometrical method. In Geometric vector addition we mainly use following two laws of vector addition: 1> Law of triangle of vector addition : The law of triangle of vector addition states: If , the two sides of a triangle represents two given vectors in magnitude and direction in same order ,...

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Vectors and Scalars

Vectors and Scalars

Vectors and Scalars: Vectors and scalars are the two classification of physical quantities in physics. Physical quantities are divided into vectors and scalars according to the range of information denoted by the quantity. Vectors: If we need to denote the motion of an object along a straight line we can take it’s motion to be positive in one direction and negative in another , But if we need to denote the motion of an object in two or three dimensions then it is not possible to denote direction of the motion using simple positive or...

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