Vector magnitude and direction question

In summary, vector C has x-component of 1 and y-component of -3. The magnitude of vector C is 3.2 and the direction is 71 degrees, 34 minutes and 36 seconds in a clockwise direction from the x-axis. The answer may also be expressed as East 72 South or between 0 and 360 degrees.
  • #1
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Homework Statement



Suppose vector C = vector A + vector B where vector A has components vector A x = 4, vector A y = 2 and vector B has components vector B x = -3, vector B y = -5.
(a) What are the x- and y- components of vector C ?

I've solved this to figure out that x = 1 and y = -3 for C

(b)What are the magnitude and direction of vector C ?
magnitude I've solved this to be 3.2
direction ? (clockwise from the x-axis) This is what I can't get. I've solved for the angle and gotten -72 degrees using tan -3/1. Does anybody know what I'm doing wrong?

Homework Equations


The Attempt at a Solution

 
Last edited:
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  • #2
Why do you say that answer is wrong. Perhaps you are not being accurate enough. 71 degrees, 35 minutes is slightly more accurate, 71 degrees, 34 minutes, and 36 seconds even more accurate. Or perhaps they want the answer in radians.
 
  • #3
It's an online problem that checks itself when you put in the answer. It's telling me that my answer of -72 degrees is wrong and I'm not sure why. Also, it wants it in degrees specifically.
 
  • #4
I've solved this to figure out that x = 1 and y = -3 for C

If X is 1 then that would be east, and given that the Y component is negative, its south.

I don't know the details of the question, but try East 72 South
 
  • #5
Perhaps they want an answer between 0 and 360 degrees.
 

1. What is the difference between vector magnitude and direction?

The vector magnitude refers to the size or length of the vector, while the direction refers to the orientation or angle of the vector in relation to a reference point.

2. How do you calculate the magnitude of a vector?

The magnitude of a vector can be calculated using the Pythagorean theorem, by taking the square root of the sum of the squares of the vector's components. For example, if a vector has components (3,4), its magnitude would be calculated as √(3^2 + 4^2) = 5.

3. Can a vector have a negative magnitude?

No, the magnitude of a vector is always a positive value. Even if the vector has negative components, the magnitude will be represented as a positive value.

4. How do you represent vector direction?

Vector direction can be represented in various ways, such as using angles, compass directions, or unit vectors. Unit vectors, also known as normalized vectors, have a magnitude of 1 and are commonly used to represent direction.

5. What is the relationship between vector magnitude and scalar multiplication?

Scalar multiplication is a mathematical operation where a vector is multiplied by a scalar, resulting in a new vector with a changed magnitude. The magnitude of the new vector is equal to the magnitude of the original vector multiplied by the scalar value.

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