subject: Define Vector Quantity [print this page] Introduction to define vector quantity: Introduction to define vector quantity:
We define the vector quantity as the force that is the vector contains magnitude and direction. The vector quantity measures the speed. We can calculate both magnitude and direction of vector quantity by using formula. The vector quantity is involved in all arithmetic operations. Now we are going to see about define vector quantity.
Explanation for Define Vector Quantity
Define vector quantity:
A force which has magnitude and direction is called as vector quantity. We must know the representation of vector quantity for measurement. Some related terms to vector quantity are,
Displacement
Direction
Velocity
Acceleration
Momentum force
Define magnitude of vector quantity:
The magnitude of vector quantity is defined as size or length of vector and it is determined by the square root of components square. The representation of vector quantity magnitude is | v |. Formulas for vector quantity magnitude are,
Single vector quantity magnitude is | v | = 'sqrt(x^2 + y^2)' .
Vector quantity magnitude with points is 'sqrt((x_(2)-x_(1))^2 + (y_(2)-y_(1))^2)' .
Define direction of vector quantity:
The vector quantity direction is represented by arrow line as 'vecAB' . The direction of vector quantity is determined by the line equation of vector. For example, Consider the line equation of vector quantity is ax + by + c = 0. The a, b and c are real numbers and the direction is (-b, a) and the multiples of (-b, a).
More about Define Vector Quantity
Example problems for define vector quantity:
Problem 1: Find out the magnitude of vector quantity.
'vecv' = (10, 4)
Solution:
The vector quantity is 'vecv' = (10, 4).
Magnitude of vector quantity is | v | = 'sqrt(x^2 + y^2)' .
= 'sqrt(10^2 + 4^2)'
= 'sqrt(100 + 16)'
= 'sqrt(116).'
| v | = 10.77
Therefore, the vector quantity magnitude is10.77
Problem 2: Find out the direction of given vector quantity equation.
2x - 5y + 3 = 0.
Solution:
The vector quantity line equation form is 2x - 5y + 3 = 0.
The AB is a two end points of line segment.
The vector quantity is represented as 'vecAB' .
'vecAB' = (5, 2).
Therefore, the direction of vector quantity is (5, 2), (25, 4)
Exercise problems for define vector quantity:
1. Find out the magnitude of vector quantity.
'vecv' = (6, 7)
Solution: The magnitude of vector quantity is 9.21
2. Find out the direction of vector quantity from 4x + 7x + 2 = 0.
Solution: The direction of vector quantity is (-7, 4), (49, 16)...
