Vectors help? How do I find a constant of this vector?

In summary, the vector V=(5i-j)+q(i+4j) is in the direction of north-east and the constant q is equal to 2. The direction of north-east suggests that the coefficients of i and j are equal, and using the example of k i + k j, it can be determined that q=2.
  • #1
xllx
33
0
The vector is this:

V=(5i-j)+q(i+4j) and it is in the direction of north-east.

I have to find the constant (q) of this vector. The part of the question before this showed that if a vector of ki+kj, where k was a positive constant is a vector of magnitude k(square root)2. So I don't know whether I have to use that in part of this answer.

I really have no idea where to start or what to do because I don't know what V is. But I was thinking about the direction, so do I have to adjust the q so that the angle is 45 degrees?

Any help at all would be greatly appreciated. Thanks.
 
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  • #2
Welcome to PF.

First I think you would want to rearrange the coefficients wouldn't you?

V = (5+q) i + (4q - 1) j

Next they tell you that the direction is Northeast.

That suggests that the coefficients of i and j are equal doesn't it?

So ...

If you wanted to find |V| (magnitude of V) then you would use what they showed with the k i + k j example.
 
  • #3
Thankyou so much!

So from that, I've managed to get q= 2.

(5+q)i = (4q-1)j
6=3q
q=2

Is this right?
Thanks again!
 
Last edited:
  • #4
xllx said:
Thankyou so much!

So from that, I've managed to get q= 2.

(5+q)i = (4q-1)j
6=3q
q=2

Is this right?
Thanks again!

Looks right to me.
 

1. What is a vector and how is it different from a scalar?

A vector is a mathematical quantity that has both magnitude and direction. This is different from a scalar, which only has magnitude. For example, velocity is a vector because it includes both speed (magnitude) and direction, while speed is a scalar because it only represents magnitude.

2. How do I represent a vector?

Vectors are typically represented by an arrow pointing in the direction of the vector with a length proportional to its magnitude. The starting point of the arrow is often labeled as the origin, and the endpoint is labeled with the coordinates (x,y) or (x,y,z) depending on the dimensionality of the vector.

3. How do I add or subtract vectors?

To add or subtract vectors, you can use the head-to-tail method or the parallelogram method. In the head-to-tail method, you align the tail of one vector with the head of the other vector, and the sum or difference is the vector that connects the tail of the first vector to the head of the second vector. In the parallelogram method, you draw two vectors from the same starting point and the sum or difference is the diagonal of the parallelogram formed by the two vectors.

4. How do I find the magnitude and direction of a vector?

The magnitude of a vector can be found using the Pythagorean theorem, which states that the magnitude is equal to the square root of the sum of the squares of its components. The direction of a vector can be found using trigonometric functions such as sine and cosine. The direction is typically measured in degrees or radians from a reference axis.

5. How do I find the constant of a vector?

The constant of a vector can be found by dividing the vector's magnitude by its direction. This will give you the ratio of the vector's magnitude to its direction, which can be used to scale the vector. For example, if you have a vector with a magnitude of 10 and a direction of 45 degrees, the constant would be 10/45, or approximately 0.222. This means that the vector can be scaled by a factor of 0.222 to reach a magnitude of 10 in the same direction.

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