Multiply a vector by a number

In this publication, we will consider how a vector can be multiplied by a number (geometric interpretation and algebraic formula). We also list the properties of this action and analyze examples of tasks.

Geometric interpretation of the work

If the vector a multiply by number m, then you get a vector b, wherein:

• b || a
• |b| = |m| · |a|
• b ↑↑ a, if m > 0, b ↑ ↓ aif m < 0

Thus, the product of a non-zero vector by a number is a vector:

• collinear to the original;
• co-directional (if the number is greater than zero) or having the opposite direction (if the number is less than zero);
• The length is equal to the length of the input vector multiplied by the modulus of the number.

The formula for multiplying a vector by a number

Product of a non-zero vector by a number is a vector whose coordinates are equal to the corresponding coordinates of the original vector, multiplied by a given number.