Vector
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 .

Example of Vector

• The Vector is also represented in Coordinates as shown above.
  The above Vector 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 = (4 - 1, 7 – 2) = (3, 5)
  Magnitude of the Vector = =.

Solved Example on Vector

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|.

Related Terms for Vector

• Components of a Vector
• Initial Point of a Vector
• Length of a Vector
• Magnitude of a Vector
• Terminal point of a Vector
• Unit Vector

Additional Links for Vector

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