===================================================Please find the attachment
DEF: A vector is a quantity that has both magnitude and direction.
DEF: A scalar is a quantity that has magnitude but NO direction.
Vector Notation A –
- Arrow above letter
– Magnitude of vector A
A vector is defined graphically by an arrow whose length is proportional to the magnitude of the vector
quantity. The direction of the arrow points in the direction of the vector quantity.
Adding Vectors Graphically
Consider adding two vectors A and B graphically. The two vectors are shown below.
1. Select an appropriate scale. (Ex. 20 cm = 5 N)
2. Draw vector A to scale and in the proper direction.
3. Draw vector B to the same scale with its tail at the tip of A and in the proper direction.
4. The resultant vector R = A + B is the vector drawn from the tail of vector A to the tip of vector B.
5. Calculate the magnitude of the resultant vector R using the selected scale and measure its direction with
6. This same process applies if you add more than two vectors.
This method of adding vectors graphically is also referred to as the
head-to-tail method, ii.
analytical method, and
Adding Vectors Using Component Method
Consider adding three 2-D vectors A, B, and C:
A = Axx+ Ayy
B = Bxx + Byy
C = Cxx + Cyy
1. Add the x-components and y-components of each vector to obtain the resultant vector R in unit vector
R = A + B + C = (Axx+ Ayy) + (Bxx + Byy) + (Cxx + Cyy)
R = (Ax + Bx + Cx) x + (Ay + By + Cy) y
Rx = Ax + Bx + Cx
Ry = Ay + By + Cy
R = Rx x + Ry y
2. Calculate the magnitude of the resultant vector R
Same procedure applies if you add more than 3 vectors. However, if the vectors are 3D,
then you must specify the direction of the resultant vector R relative to the positive x, y,
and z axis.
1. A car travels 20 mi at 600 north of west, then 35 mi at 45o north of east.
2. Express each displacement vector in unit vector notation. Take the +x-axis due east and the
+y-axis due north.
3. Use the component method to obtain the resultant displacement vector in unit...