Find the scalar product of the vectors in Figure P7.8, where è = 117° and F = 31.0 N.
y
|
|
___|
Unk Angle----> / |
-------\--------------x
starts@O-----> / /| /
/ /_|/<-----117 degrees
/ / |
/ / <-----31.0N
To find the scalar product of two vectors, you need to multiply their magnitudes and the cosine of the angle between them.
In this case, the magnitude of vector F is given as 31.0 N, and the angle between the two vectors is given as 117 degrees.
1. Calculate the x and y components of vector F:
- The x component of vector F is F * cos(117°).
- The y component of vector F is F * sin(117°).
2. Use the x and y components of vector F and the given angle to determine the x and y components of the unknown vector:
- The x component of the unknown vector is equal to the x component of vector F. (Since they are aligned in the same direction)
- The y component of the unknown vector is equal to the y component of vector F, but with the same magnitude and opposite sign.
3. Calculate the magnitudes of both vectors:
- The magnitude of vector F is given as 31.0 N.
- The magnitude of the unknown vector can be calculated using the Pythagorean theorem: sqrt(x^2 + y^2).
4. Calculate the scalar product of the two vectors:
- The scalar product is the product of the magnitudes of the vectors and the cosine of the angle between them.
- So, scalar product = magnitude of unknown vector * magnitude of vector F * cos(117°).
You can now follow these steps to calculate the scalar product of the vectors in Figure P7.8.
I cannot make any sense of that.
Unfortunately, what you type is not what you get.
there are two vectors in quadrant three
one with a magnitude of 31.0N and has a direction of 117degrees in the negative direction from the x axis the other has an unknown magnitude and unkown theta in the positive direction starting from 90 degrees