explain the concept of components of a vector?

Answer 1

OK!

A vector has two components: size (magnitude) and direction.

Think about velocity. A car traveling down a straight road has a speed (how fast) and a direction. Together, the car's velocity is described by a vector, e.g., 55 mph due west.

Answer 2

A vector has 2 attributes a importance and a course. The course could be expressed in 2 or 3 dimensional area. each and each vector could be broken down into factors (making use of common trigonometry) alongside the X, Y, and Z axis of area to make the diagnosis of forces performing upon an merchandise much less stressful to visualise and calculate the sum of the the forces. in ballistic action, projectile shuttle in a predictable arc. the preliminary forces are the perspective and tension with which the object bypass away the barrel of the firing mechanism and gravity. making use of trigonometry we are able to in spite of the preliminary perspective wreck the launching tension into X, and Y factors. The Y component will act as we talk opposite gravity and could with the aid of the years decay the vertical component until the object returns to "earth". The X component assuming no friction won't decay and could tell how a techniques away the projectile will land.

Answer 3

A vector has length and direction. For example a vector in a coordinate system could start at the origin (0,0) and extend to the point (3,4). In this case its length would be 5 units. Its horizontal component would be 3 and its vertcal component would be 4.

In other words, you could get from (0,0) to (3,4) by following the direct route of the vector, or you could get there by first going 3 units directly East and the 4 units directly North. In the latter case, you would travel along the components of the vector.

Answer 4

In physics and in vector calculus, a spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. A vector has properties that do not depend on the coordinate system used to describe it. However, a vector is often described by a fixed number of components, each of which is dependent upon the particular coordinate system being used, such as Cartesian coordinates, spherical coordinates or polar coordinates.

Answer 5

A vector is a direction with a length (also called the magnitude). A vector can be in any dimenshion but the second dimenshion is the easiest to imagine. If you think about a 2D graph with cartesian coordinates (just like regular graph paper) and draw a line from (0,0) outward, it can be a vector.

So for example, if you draw a line from (0,0) to (2,1) your vector has coordinates (2,1). 2 is the x coordinate, 1 is the y coordinate. So if you got a vector like (34, 125) then you know to draw the vector from (0,0) to (34,125). When we mention the components (35,125), we don't need to say from (0,0) because that is implied.

Answer 6

Basically, an n-dimensional vector has n components - one for each of the dimensions represented by the vector. For example, in a 2-dimensional vector, the two components represent the distance in the directions of the coordinate axes.

Answer 7

A vector is a magnitude (ex. speed) and a direction (ex. Northwest or 45 degrees north of west). If you were driving northwest at 55 mph for one hour, you would end up 55 miles NW from where you started.

Say you wanted to take a different path but end up at the same place. You could use components to figure out how far north to travel and how far west to travel. In the example given, you would need to travel 38.89 miles north and 38.89 miles west. You can see that would require you to travel 77.78 miles, instead of 55 miles, but you would end up in the same place either way.

Vector components are very useful in the addition of vectors. (ex. adding forces to find the net force, adding velocities to find the net velocity)