Math Homework. Do It Faster, Learn It Better.
Scalar Multiplication of Vectors
To multiply a vector by a scalar, multiply each component by the scalar.
If has a magnitude and direction , then where is a positive real number, the magnitude is , and its direction is .
Note that if is negative, then the direction of is the opposite of .
Example :
Let , Find .
Properties of Scalar Multiplication:
Let and be vectors, let and be scalars. Then the following properties are true.
Properties of Scalar Multiplication
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The magnitude of the scaled vector is equal to the absolute value of the scalar times the magnitude of the vector. | |
Associative Property | |
Commutative Property | |
Distributive Property |
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Identity Property | |
Multiplicative Property of | |
Multiplicative Property of |