Definition Of Vector

Any quantity that has both magnitude and direction is called a vector.

More About Vector

A vector is always shown by an arrow when it is represented by a line segment.
Force and velocity are vector quantities
The starting point of a vector is known as initial point and the end point is known as terminal point.
Magnitude of a vector is given as 

Video Examples: What is a vector?

Example of Vector

The vector is also represented in coordinates as shown above.
The above vector v has A (1, 2) as the initial point and B (4, 7) as the terminal point.
The component form of the vector represented by the directed line segment from A (x₁, y₁) to B (x₂, y₂) is (x₂ - x₁, y₂ - y₁).
The component form of the vector v = (4 - 1, 7 - 2) = (3, 5)
Magnitude of the vector v =  = 

Solved Example on Vector

Ques: Let u = <6, 8=""> and v = <24, 32=""> be two vectors. Which of the following is correct for u and v?

Choices:

A. 4|u| = |v|
B. |u| = |v|
C. |u| = 4|v|
D. 5|u| = |v|
Correct Answer: A

Solution:

Step 1: u = <6, 8="">, v = <24, 32=""> are the two vectors.
Step 2: |u| =  = 10 [Use the formula to find the magnitude of u.]
Step 3: |v| =  = 40 [Use the formula to find the magnitude of v.]
Step 4: So, 4|u| = |v|.

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