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

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Homework Help Overview

The discussion revolves around a vector expressed as V=(5i-j)+q(i+4j), where the goal is to determine the constant q given that the vector points in the direction of north-east. Participants are exploring the implications of this direction on the components of the vector.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss rearranging the vector components and consider the condition that the coefficients of i and j must be equal for the vector to point northeast. There is also a mention of using the magnitude of the vector in relation to its direction.

Discussion Status

Some participants have made progress in determining the value of q, with one suggesting that they found q=2 based on the equality of the vector components. However, there is no explicit consensus on the correctness of this value, as further validation is not provided.

Contextual Notes

There is a reference to a previous part of the question that discusses the magnitude of vectors, which may influence the understanding of the current problem. Additionally, the participants are navigating the implications of the vector's direction on the values of its components.

xllx
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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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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.
 
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:
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.
 

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