Vectors
Calculating the Modulus of a Vector
In this section, you will learn how to calculate the modulus of a vector. The modulus is a mathematical term for the length or the magnitude.
This video and text below takes a look at Vectors and Scalars.
The magnitude of vector x is written as |x|.
The magnitude of vector
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is written as |AB|.
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Zero vector and unit vectors
A vector with magnitude 0 is called the zero vector, written 0. A vector with magnitude 1 is called a unit vector.
Vectors are equal if they have the same magnitude and the same direction.
a = b
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Inverse Vectors
The inverse of a vector is a vector of equal magnitude but in the opposite direction. The inverse of
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is -
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or
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and the inverse of a is -a.
Scalars
Scalars have magnitude but not direction. Vectors can be multiplied by a scalar to produce another vector.
Multiplying vector x by 3 will give a new vector 3 times the length and parallel to x.
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Vector addition and subtraction
When 2 vectors are added or subtracted the vector produced is called the resultant.
The resultant is identified by a double arrowhead.
Triangle Law:
To add two vectors you apply the first vector and then the second.
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+
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=
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or
a + b = c
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Subtracting a vector is the same as adding its inverse.
a – b is the same as a + (-b)
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Parallelogram Law:
Moving from A to C through B is the same as moving through D.
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+
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=
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+
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=
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or
a + b = b + a = c
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