Interpreting Vector Directions: A=8 at 45°, B=8 at 180/225°

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In summary, vector A has a magnitude of 8 units and makes an angle of 45 degrees with the positive x axis. Vector B also has a magnitude of 8 units and points in the opposite direction of A, making an angle of 180 degrees with the positive x axis. This is the same as saying vector B points in the negative x direction.
  • #1
Skotster
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Am I interpreting this question correctly?

Vector A has a magnitude of 8 units and makes an angle of 45 degrees with the positive x axis. Vector B also has a magnitude of 8 units but points in the -x direction. ...

So, does that mean:

Vector A=8 at 45 degrees
Vector B=8 at 180 degrees

or

Vector A=8 at 45 degrees
Vector B=8 at 225 degrees

I know how to do the problem, it's just interpreting the book's wording on angles.

Thanks
 
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  • #2
A at 45 degrees and B at 180 degrees. Saying vector B points in the -x direction is the same as saying vector B makes an angle of 180 degrees with the +ve x axis.
 
  • #3
Thanks much
 
  • #4
225 degrees would be opposite to A's direction not in "the -x direction. ... "
 

1. What do the numbers and symbols in the vector equation represent?

The numbers represent the magnitude or size of the vector, while the symbols represent the direction. In this case, the "A" vector has a magnitude of 8 and a direction of 45 degrees, and the "B" vector has a magnitude of 8 and a direction of 180/225 degrees.

2. How do you interpret the direction of a vector?

The direction of a vector is given by the angle it makes with the positive x-axis. In this case, the direction of the "A" vector is 45 degrees, which means it points in the northeast direction. The direction of the "B" vector is 180/225 degrees, which means it points in the south direction.

3. How do you calculate the resultant of two vectors?

To calculate the resultant of two vectors, you can use the Pythagorean theorem and trigonometric functions. First, calculate the sum of the x-components and the y-components of the vectors. Then, use the formula R = √(Rx² + Ry²) to find the magnitude of the resultant. Finally, use the formula θ = tan^-1 (Ry/Rx) to find the direction of the resultant.

4. What is the difference between a scalar and a vector?

A scalar is a quantity that only has magnitude, while a vector has both magnitude and direction. Scalars can be represented by a single number, while vectors need to be represented by magnitude and direction.

5. Can two vectors with the same magnitude have different directions?

Yes, two vectors with the same magnitude can have different directions. In fact, in the given vector equation, both "A" and "B" have a magnitude of 8, but they have different directions of 45 degrees and 180/225 degrees, respectively.

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