Co-ordinates of point P in (x,y) plane are x and y. Position vector 1 of this point makes angle with X-axis.
unit vectors ñr and ñe (in XY plane) which are parallel and perpendicular to r respectively.
Answers
Answer:
Vectors are usually described in terms of their components in a coordinate system. Even in everyday life we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if you ask someone for directions to a particular location, you will more likely be told to go 40 km east and 30 km north than 50 km in the direction
37
°
north of east.
In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is described by a pair of coordinates (x, y). In a similar fashion, a vector
→
A
in a plane is described by a pair of its vector coordinates. The x-coordinate of vector
→
A
is called its x-component and the y-coordinate of vector
→
A
is called its y-component. The vector x-component is a vector denoted by
→
A
x
. The vector y-component is a vector denoted by
→
A
y
. In the Cartesian system, the x and y vector components of a vector are the orthogonal projections of this vector onto the x– and y-axes, respectively. In this way, following the parallelogram rule for vector addition, each vector on a Cartesian plane can be expressed as the vector sum of its vector components:
→
A
=
→
A
x
+
→
A
y
.
As illustrated in (Figure), vector
→
A
is the diagonal of the rectangle where the x-component
→
A
x
is the side parallel to the x-axis and the y-component
→
A
y
is the side parallel to the y-axis. Vector component
→
A
x
is orthogonal to vector component
→
A
y
.
Vector A is shown in the x y coordinate system and extends from point b at A’s tail to point e and its head. Vector A points up and to the right. Unit vectors I hat and j hat are small vectors pointing in the x and y directions, respectively, and are at right angles to each other. The x component of vector A is a vector pointing horizontally from the point b to a point directly below point e at the tip of vector A. On the x axis, we see that the vector A sub x extends from x sub b to x sub e and is equal to magnitude A sub x times I hat. The magnitude A sub x equals x sub e minus x sub b. The y component of vector A is a vector pointing vertically from point b to a point directly to the left of point e at the tip of vector A. On the y axis, we see that the vector A sub y extends from y sub b to y sub e and is equal to magnitude A sub y times j hat. The magnitude A sub y equals y sub e minus y sub b.