How do you change the magnitude of a vector?

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Homework Help Overview

The discussion revolves around vector operations, specifically focusing on the addition of vectors and changing their magnitudes. The original poster presents a problem involving three vectors and seeks assistance with two specific parts related to vector magnitude and linear combinations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the addition of vectors and the concept of unit vectors. Questions are raised about how to determine the magnitude of a vector and the implications of scaling vectors. There is also discussion about the linear combination of vectors and how to set up equations based on vector components.

Discussion Status

The discussion includes various attempts to clarify the definitions and relationships between the vectors. Some participants suggest checking the magnitudes and using geometric relationships, while others are focused on understanding the implications of the linear combination of vectors. There is no explicit consensus, but several productive lines of inquiry are being explored.

Contextual Notes

Participants are working within the constraints of a homework assignment, which may limit the information available for solving the problem. There is an emphasis on understanding the concepts rather than providing direct solutions.

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Three vectors a, b and c are such that a = i + 3j, b = 2i + j and c = i + 13j. Find
(i) the vector which is parallel to a + b and of magnitude 20 units.
(ii) the value of p and of q for which pa + qb = c

I need help in both parts.
 
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i)

what is a+b ?

Then, what is the definition of a unit vector? And then how do you change the magnitude of a vector?

ii) What does pa mean, and qb mean? You will have two equations. One will solve the c i component, the other will solve the c j component.
 
what is the magnitude of a + b?
you need a vector of maginutude 20, in the same direction of a + b.
the scale of your magnitudes should be the same as the scale of your components. (check it for yourself - can you see it's just similar triangles?)

look out for this nice 3,4,5 triangle; they can simplify calculations if you spot them.
i.e where two sides are of length 3 and 4 units, while the hypotenuse is 5 units. that is, if you have a triangle with two of the sides being any two of these numbers, you know immediately the other side must be the missing number.
5,12,13 is another one to look out for. a bit trickier to spot.
These pop up frequently!
 
Last edited:
Thank you.
 

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