Vectors, dot products and determining the values

In summary, the conversation discusses vectors a, b, and c forming a triangle. The values of a dot b - a dot c - b dot c are being determined, given that |a| = 1, |b| = 2, and |c| = 3. The conversation also suggests drawing the triangle and applying the law of cosines to find the answer.
  • #1
bngo93
4
0
vectors a - b + c = 0 ,determine the values of a dot b - adot c - b dot c if

|a|=1, |b|=2 and |c|=3
 
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  • #2
Have you tried anything so far?

Let's say you have for example vectors w, x, y, if you have x*y + w*y, it is the same as y*(x+w), where * indicates dot product and x+w is the sum of both vectors.
 
  • #3
oh i have no idea how to start this problem my first attempt was horrible

i just changed the |a| to a*a by squaring both sides
i don't know if I am on the right track but ill just try and see where it leads
It leads to a dead end : [
 
Last edited:
  • #4
im lost ;/
 
  • #5
Draw -a, b and c on a piece of paper. They form a triangle. Can you say anything special about this triangle??
 
  • #6
umm would the values be the ones listed? with the magnitudes
and how did u get -a??
 
  • #7
I get the feeling micromass meant to say a, -b, and c. I also think he was getting at this: what would the sides of the triangle be?
 
  • #8
Yes, I believe micromass meant a, -b, c.
Actually, a triangle is not quite the right word to describe
how the vectors a, -b, c relate to each other.
An improved question:
if we attempt to draw that triangle, what figure do we get?

Hopefully, the answer will be clear, once you have the correct figure. However, if necessary, apply law of cosines
Google can be a good refresher or
http://mathworld.wolfram.com/LawofCosines.html

Please let us know what figure you get, & if you still need help after drawing the figure.
 

1. What are vectors and how are they represented?

Vectors are mathematical objects that have both magnitude and direction. They can be represented geometrically as arrows with a certain length and direction, or algebraically as an ordered list of numbers.

2. How are dot products calculated?

The dot product, also known as the scalar product, is a mathematical operation between two vectors that results in a single scalar value. It is calculated by multiplying the corresponding components of the vectors and then adding them together.

3. What is the significance of the dot product?

The dot product has several important applications in mathematics and physics. It can be used to find the angle between two vectors, determine if two vectors are perpendicular, and calculate the projection of one vector onto another.

4. How do you determine the values of vectors using dot products?

To determine the values of vectors using dot products, you can set up a system of equations and solve for the unknown variables. This can be done by setting the dot product of two vectors equal to a known value and then solving for the unknown variables.

5. Can the dot product be negative?

Yes, the dot product can be negative. This occurs when the angle between two vectors is greater than 90 degrees, which means the vectors are pointing in opposite directions. In this case, the dot product is negative because the two vectors are "opposed" to each other.

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