# Multiplication Of A Vector By A Real Number

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When we multiply a vector A by a real number λ, then we get a new vector along the direction of vector A. Its magnitude becomes λ times the magnitude of the given vector.

Similarly, if we multiply a vector A by a real number -λ, then we get a new vector whose magnitude is λ times the magnitude of the vector A but direction is opposite to that of vector A.

Example:- Consider a vector A is multiplied by a real number λ = 3 and λ = -4

### Resultant Vector

The resultant vector of two or more vectors is defined as the single vector which produces the same effect as two or more vectors combinely produces.

Case-I: When two vectors are acting in the same direction

Let the vector A and B are acting in the same direction.

The resultant of this two vectors is given by a vector having direction as same of A or B and the magnitude of the resultant vector will be equal to the sum of the respective vectors.

Thus, the resultant vector R = A+B

Case-II: When two vectors are acting in mutually opposite directions.

Let vector A and B are acting in mutually opposite direction.

Then, the resultant of these two vectors is given by a vector having direction same as that of vector with larger magnitude. The magnitude of resultant vector will be equal to |A-B|.

Thus, the resultant vector R = A-B

If B>A, then direction of R is along B.

If A>B, then the direction of R is along A.