Question

15 importance of vector quantites

Answer 1

Vector Quantities

Vector quantities, however, refer to both the direction of the medium’s movement as well as the measurement of the scalar quantity.

Increase/Decrease in Temperature - The measurement of the medium’s temperature is a scalar quantity; the measurement of the increase or decrease in the medium’s temperature is a vector quantity.

Velocity - The measurement of the rate at which an object changes position is a vector quantity. For example:

If a person quickly moves one step forward and then one step backward there would certainly be a lot of activity; but, there would be "zero velocity."

In order to measure the vector quantity of the medium, there must be:

A directional measurement applied to the scalar quantity. For example:

Regardless of how fast an object is going, the direction of the movement must be described in the velocity vector such as "rightwards" or "forward."

A beginning reference point for the directional measurement in order to provide the directional element of the vector quantity. Your beginning point could be centered in a north, south, east and west quadrant so that the vector quantity can be applied to the medium’s movement. For example:

To describe a car's velocity you would have to state it as 70 miles per hour, south.

Another directional element that may be applied to the vector quantity is the different between vertical and horizontal movements.

Answer 2

A VECTOR is a universal component that can be used to quantify how a FORCE, or ACTION, is applied to a structure, truss, beam or a number of other applications we will encounter.

Using the scenario of a golf club striking a golf ball, a few ways that we can apply VECTORS are:

· A VELOCITY VECTOR can describe the velocity motion of a golf ball

· A DISTANCE VECTOR can help determine how far away and in what direction a golf ball lands

· A FORCE VECTOR can describe how hard and in what direction the golf club strikes the golf ball

When performing engineering calculations and analysis utilizing VECTOR MECHANICS, we assume that the bodies and particles of interest are RIGID BODIES, and will not deform under load.

STATICS is the study of VECTOR MECHANICS that deals with bodies under action of forces that are either at rest or move with a constant velocity.

DYNAMICS is the study of motion of bodies under accelerated motion.

VECTORS are commonly represented in VECTOR NOTATION, where a SCALAR is used to represent the component of each quantity with respect to a particular axis or direction.

A vector representing 3 components, or dimensions, can be expressed in VECTOR NOTATION as:

Let’s highlight some of the more important CHARACTERISTICS of note:

·A SCALAR is a mathematical quantity that retains a magnitude only, whereas, a vector is one that possesses both magnitude and direction.

·The SENSE of a vector is the SIGN OF THE MAGNITUDE, or the direction in which the vector is acting. The sense is the part of a vector that indicates whether a football thrown is coming towards you or away from you.

·The POINT OF APPLICATION is the physical location on the object or in space where the vector is acting. The LINE OF ACTION represents the line space on which the vector is acting.

·The HEAD is the vector’s sense and is indicated by the arrowhead.

·The TAIL of the arrow typically depicts the vector’s point of application.

·The SHAFT is the actual line-length of the arrow representing the vector’s magnitude, where a longer vector drawing implies a large action and vice versa.

·The LABEL of the vector helps to label or distinguish the vector from other vectors in the analysis.

Two vectors are said to be the same if they have the same MAGNITUDE and DIRECTION. However, they can be anywhere in space, and do not need to have the same point of application.

A NEGATIVE VECTOR is a vector with the same magnitude, but OPPOSITE DIRECTION.

HOPE IT HELPS.....