Why do we use vectors

A quantity that has magnitude and direction is called a vector. Vectors have many real-life applications, including situations involving force or velocity. For example, consider the forces acting on a boat crossing a river. Both forces are vectors. Learning Objectives Distinguish the difference between the quantities scalars and vectors represent. Key Takeaways Key Points Scalars are physical quantities represented by a single number and no direction.

Vectors are physical quantities that require both magnitude and direction. Examples of scalars include height, mass, area, and volume. Examples of vectors include displacement, velocity, and acceleration. Key Terms Coordinate axes : A set of perpendicular lines which define coordinates relative to an origin. Example: x and y coordinate axes define horizontal and vertical position.

Adding and Subtracting Vectors Graphically Vectors may be added or subtracted graphically by laying them end to end on a set of axes.

Learning Objectives Model a graphical method of vector addition and subtraction. Key Takeaways Key Points To add vectors, lay the first one on a set of axes with its tail at the origin. When there are no more vectors, draw a straight line from the origin to the head of the last vector.

This line is the sum of the vectors. To subtract vectors, proceed as if adding the two vectors, but flip the vector to be subtracted across the axes and then join it tail to head as if adding. Adding or subtracting any number of vectors yields a resultant vector. Key Terms origin : The center of a coordinate axis, defined as being the coordinate 0 in all axes.

Coordinate axes : A set of perpendicular lines which define coordinates relative to an origin. Adding and Subtracting Vectors Using Components It is often simpler to add or subtract vectors by using their components. Learning Objectives Demonstrate how to add and subtract vectors by components. Key Takeaways Key Points Vectors can be decomposed into horizontal and vertical components.

Once the vectors are decomposed into components, the components can be added. Adding the respective components of two vectors yields a vector which is the sum of the two vectors. Key Terms Component : A part of a vector.

For example, horizontal and vertical components. Multiplying Vectors by a Scalar Multiplying a vector by a scalar changes the magnitude of the vector but not the direction. Learning Objectives Summarize the interaction between vectors and scalars.

Key Takeaways Key Points A vector is a quantity with both magnitude and direction. A scalar is a quantity with only magnitude. The vector lengthens or shrinks but does not change direction.

Key Terms vector : A directed quantity, one with both magnitude and direction; the between two points. Example For example, if you have a vector A with a certain magnitude and direction, multiplying it by a scalar a with magnitude 0.

Multiplying a vector by a scalar is the same as multiplying its magnitude by a number. Learning Objectives Predict the influence of multiplying a vector by a scalar. Key Takeaways Key Points A unit vector is a vector of magnitude length 1. A scalar is a physical quantity that can be represented by a single number. Unlike vectors, scalars do not have direction.

Key Terms scalar : A quantity which can be described by a single number, as opposed to a vector which requires a direction and a number. Position, Displacement, Velocity, and Acceleration as Vectors Position, displacement, velocity, and acceleration can all be shown vectors since they are defined in terms of a magnitude and a direction.

Learning Objectives Examine the applications of vectors in analyzing physical quantities. Key Takeaways Key Points Vectors are arrows consisting of a magnitude and a direction. They are used in physics to represent physical quantities that also have both magnitude and direction. Displacement is a physics term meaning the distance of an object from a reference point.

Since the displacement contains two pieces of information: the distance from the reference point and the direction away from the point, it is well represented by a vector. Velocity is defined as the rate of change in time of the displacement. To know the velocity of an object one must know both how fast the displacement is changing and in what direction.

Therefore it is also well represented by a vector. Acceleration, being the rate of change of velocity also requires both a magnitude and a direction relative to some coordinates. Key Terms velocity : The rate of change of displacement with respect to change in time. Or the cars could have been travelling in opposite directions, in which case it was a head on collision with a relative velocity between the cars of mph! Why are vectors important in physics? Physics 2D Motion Introduction to Vectors.

Daniel W. Jul 15, Related questions Why is a vector product perpendicular? If I push your right shoulder hard enough you will turn one way and if I push your left shoulder with a force of the same magnitude in the same direction an equal vector you will turn the other way. The two forces have different turning effects so they are different forces even though they have the same 'vector properties'.

When we add forces we simply use their vector properties but to specify a force we need to give its magnitude, direction and line of action. To add position vectors we simply add the components. What about subtraction? The effect of adding these two vectors is to give the zero vector. The equivalent method of subtraction for free vectors can be thought of as reversing the vector to be subtracted and adding it to the first vector.

One of the uses of multiplication of vectors by scalars is to write down an equation of a line using vectors. Main menu Search. An Introduction to Vectors.