Solving a Dot Product Vector Problem (-1,0)

In summary, the conversation discusses finding two vectors, v1 and v2, whose sum is (-1,0) where v1 is parallel to (5,-5) and v2 is perpendicular to (5,-5). The first step is to write the unknown vectors in terms of their components, v1=(x1,y1) and v2=(x2,y2). The fact that v1+v2 must equal (-1,0) provides a condition to solve for the unknown components. The conversation then mentions the dot product and its relation to perpendicularity, but ultimately asks for help in solving the problem.
  • #1
ih8calc
4
0
Hello, I have this problem that asks the following

Homework Statement


Find two vectors v1 and v2 whose sum is (-1,0) where v1 is parallel to (5,-5) while v2 is perpendicular to (5,-5).

Could someone "walk" me thought the steps to find v1 and v2... I'm confident I can make the computations is the steps that are unknown to me... thanks in advance...
 
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  • #2
If v1 is parallel to (5,-5) then v1 = (k5,-k5). k is an unknown that you will need to solve for.

A similar setup applies to v2. v2 is perpendicular to (5,-5) so it is parallel to (5,5).
 
  • #3
The first step would be to write the unknown vectors in terms of there unknown components: [itex]v_1=(x_1,y_1)[/itex] and [itex]v_2=(x_2,y_2)[/itex]...what is [itex]v_1+v_2[/itex] in terms of these components?...what does the fact that this vector sum must be (-1,0) tell you?
 
  • #4
...okay, so maybe I can't follow directions as well as I thought... I hate to ask, but could you solve it for me? it's one of those things where I'm just stumped...
 
  • #5
Why don't you show us what you've got? (even if you think it is wrong)
 
  • #6
ih8calc said:
...okay, so maybe I can't follow directions as well as I thought... I hate to ask, but could you solve it for me? it's one of those things where I'm just stumped...
Since you titled this "dot product" why don't you tell us what you think the dot product is and how it is related to "perpendicular".
 

1. What is a dot product vector problem?

A dot product vector problem involves finding the scalar or numerical value of the dot product between two given vectors. The dot product is a mathematical operation that takes two vectors and produces a scalar value. It is also known as the scalar or inner product.

2. How do you solve a dot product vector problem?

To solve a dot product vector problem, you need to first calculate the dot product formula, which involves multiplying the corresponding components of the two vectors and adding them together. For example, if we have two vectors A = (a1, a2) and B = (b1, b2), the dot product formula would be a1*b1 + a2*b2. Then, plug in the values of the given vectors and solve for the scalar value.

3. What is the purpose of solving a dot product vector problem?

Solving a dot product vector problem can help us find the angle between two vectors, determine if two vectors are perpendicular or parallel, and calculate the projection of one vector onto another. It has many applications in physics, engineering, and computer graphics.

4. What are the common mistakes when solving a dot product vector problem?

One common mistake is forgetting to multiply the corresponding components and instead adding them together. Another mistake is using the wrong formula, such as using the cross product formula instead of the dot product formula. It is also important to pay attention to the order of the vectors when plugging in values.

5. Can a dot product be negative?

Yes, a dot product can be negative. The dot product value depends on the angle between the two vectors. If the angle between the vectors is greater than 90 degrees, the dot product will be negative. If the angle is less than 90 degrees, the dot product will be positive. If the angle is exactly 90 degrees, the dot product will be zero.

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