Question about the direction of a vector

Let's start with a sketch. First we have A and B (3,-6) and (4,-5) in blue and green.The difference vector A - B is the vector from the tip of B to the tip of A. This is shown in purple. The direction of the vector is the angle with respect to the positive x-axis, which is shown in red. We can see that this angle is approximately 225 degrees. So in summary, the direction of the vector C = A - B is at an angle of 225 degrees.
  • #1
Sall1230
10
0

Homework Statement


Let A= 3i - 6j and B= 4i - 5j. The direction of the vector C = A - B is at an angle of?

Homework Equations


Magnitude= ( a^2 + b^2 ) ^1/2
Tan^-1 = b/a

The Attempt at a Solution


A-B =
3-4 i -6--5j
-1i -1j
Tan^-1 = -1/-1 = 45
45+180 = 225

Is this correct?
 
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  • #2
Sall1230 said:
A-B =
3-4 i -6--5j
-1i -1j
Tan^-1 = -1/-1 = 45
45+180 = 225

Is this correct?
You really need to work on your notation here, the first line is missing parentheses or basis vectors for two terms, there is no equality sign between the second line and the third line, the inverse tangent function has no argument and -1/-1 is 1 and not 45.

That being said, what you are actually doing (which is not what you are writing) is correct.
 
  • #3
As this is a 2D problem it's not hard to draw it.
 

Related to Question about the direction of a vector

1. What is a vector?

A vector is a quantity that has both magnitude and direction. It is often represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction.

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

The direction of a vector can be determined by using the concept of angles. The angle between the vector and a reference line, such as the x-axis, is known as the direction angle. It is measured in degrees or radians.

3. How do you represent the direction of a vector mathematically?

The direction of a vector can be represented mathematically using trigonometric functions such as sine, cosine, and tangent. These functions can be used to find the direction angle of a vector.

4. Can a vector have a negative direction?

Yes, a vector can have a negative direction. This simply means that the vector is pointing in the opposite direction of the positive direction, which is usually defined as the direction of the x-axis.

5. How do you add or subtract vectors in different directions?

To add or subtract vectors in different directions, you can use the parallelogram law or the head-to-tail method. These methods involve drawing the vectors as arrows, with their tails connected, and using basic geometric principles to determine the resulting vector.

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