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In mathematics and physics, a vector is an element of a vector space.
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Vectors, are objects which have both, magnitude and direction.
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Magnitude defines the size of the vector.
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It is represented by a line with an arrow, where the length of the line is the magnitude of the vector and the arrow shows the direction.
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Two vectors are said to equal if their magnitude and direction are the same.
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A vector can be added to another vector, head to tail.
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The order of addition of two vectors does not matter, because the result will be the same.
- A vector from point "A" to "B" would be like
, Which is a positional vector.
- The magnitude of a vector is shown by vertical lines on both the sides of the given vector “|a|”.
- It represents the length of the vector. Mathematically, the magnitude of a vector is calculated by the help of “Pythagoras Theorem,” i.e.
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A unit vector has a length (or magnitude) equal to one,
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which is basically used to show the direction of any vector.
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A unit vector is equal to the ratio of a vector and its magnitude.
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Symbolically, it is represented by a cap or hat (^).
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If a is vector of arbitrary length and its magnitude is ||a||, then the unit vector is given by:
- It is also known as normalising a vector.
- Suppose from the above solution we need to find out the Unit vector of AB
A vector with zero magnitudes is called a zero vector. The coordinates of zero vector are given by (0,0,0) and it is usually represented by 0 with an arrow (→) at the top or just 0.
- We can do vector operations such as Addition, Subtraction, Multiplication on vectors.