vector function is denoted by or

has both magnitude (length) and direction. Magnitude and direction is defined by components of a vector.

Vector-Valued Functions or Vector Function

Vectors are made of components. When you break a vector into parts, the parts are called components.

Each part of a two-dimensional vector, say <4, 5> corresponds to the x-axis (horizontal) component is 4,

and the y-axis (vertical) component is 5. This means your path is towards 4 on x-axis and towards 5, up

(vertical) on y-axis. In the two dimensional figure below, the vector “v” in the component form is written as

v = <vx , vy> => v = <4.5>.

Each part of a two-dimensional vector, say <4, 5> corresponds to the x-axis (horizontal) component is 4,

and the y-axis (vertical) component is 5. This means your path is towards 4 on x-axis and towards 5, up

(vertical) on y-axis. In the two dimensional figure below, the vector “v” in the component form is written as

v = <vx , vy> => v = <4.5>.

For example, if we draw a t axis with ‘a’, ‘b’ end points and at some instance we have t0; that is the place of the fly at that moment. Then

there is a vector corresponding to that particular time t0.

there is a vector corresponding to that particular time t0.

We give this function a name-- and we show the various paths of the fly at particular time through vector (ta)--start point,

(t0)--snapshot point and (b)--end point. (t0) is pronounced as**r of t0.**

In the picture below, fly starts at end point t(a), changes direction and stops at t(b). On the flight path, we have a snap shot at t(0). The curve

is C and can be measured for its length.

(t0)--snapshot point and (b)--end point. (t0) is pronounced as

is C and can be measured for its length.

Typically, a physics problem gives you an angle and a magnitude to define a vector and you have to find

the components of vector using trigonometry. In the case of a ball rolling on a table, it can roll at an angle

θ and the magnitude will be the speed at which the ball is rolling.

the components of vector using trigonometry. In the case of a ball rolling on a table, it can roll at an angle

θ and the magnitude will be the speed at which the ball is rolling.

In some books the vector function is given by the following equation:

Source: http://www.youtube.com/watch?v=5ymFpq7PPxM

Equation is parametric form and rectangular form?

We hope that this tutorial moves faster than watching a video tutorial. Where credit for the material used in this tutorial

is due, we have provided. In a few places some of the images shown below are not our original work. We have

misplaced the credits as we were building this web page. However, we have made notification on these images to

explain the concept further.

is due, we have provided. In a few places some of the images shown below are not our original work. We have

misplaced the credits as we were building this web page. However, we have made notification on these images to

explain the concept further.

Vector function gives you a history on a path of a curve. Think of a fly trained to take a certain path, which is the curve. You can trace

through vectors where the fly was at a particular time. If you have two flies, you will have two histories on the same curve. Vectors are

snap shots of a particular time.

through vectors where the fly was at a particular time. If you have two flies, you will have two histories on the same curve. Vectors are

snap shots of a particular time.