Find the resultant of two vectors 9 units and 8 units acting at a point 0 at an angle of 45degree with each other

Question

A. Scale drawing
B. Analytical method

Answer 1

To find the resultant of two vectors using a scale drawing:
1. Draw a vector representing one of the given vectors. In this case, draw a vector of 9 units in length.
2. From the tip of this vector, draw a second vector representing the second given vector. In this case, draw a vector of 8 units in length at an angle of 45 degrees from the first vector.
3. Label the initial point of both vectors as "O" and the endpoint of the second vector as "R".
4. Draw a straight line from the initial point "O" to the endpoint "R" of the second vector.
5. Measure the length of this line. This represents the magnitude of the resultant vector.
6. Draw an arrow on this line to indicate the direction of the resultant vector.
7. Label the magnitude and direction of the resultant vector.

To find the resultant of two vectors using the analytical method:
1. Represent one of the given vectors as a complex number. In this case, let the first vector be 9 units long, and we will represent it as 9 + 0i.
2. Represent the second vector as a complex number using the given angle. In this case, let the second vector be 8 units long at an angle of 45 degrees. Using trigonometry, we can represent this vector as (8 * cos(45)) + (8 * sin(45))i.
3. Add the two complex numbers together to find the resultant vector: (9 + 0i) + ((8 * cos(45)) + (8 * sin(45))i).
4. Simplify the complex number to find the magnitude and direction of the resultant vector.