Find Values of a and b for Perpendicular Vectors

In summary, the conversation discusses finding the values of a and b so that two given vectors, v and w, are perpendicular. The equations a - (a.b)b and sqrt(a^2+13) = sqrt(b^2+5) are mentioned as possible ways to solve the problem. The conversation also hints at using a simple operation to determine perpendicularity.
  • #1
noahsdev
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Homework Statement



If [itex]\underline{v}[/itex] = a[itex]\underline{i}[/itex] + 2[itex]\underline{j}[/itex] + 3[itex]\underline{k}[/itex] and [itex]\underline{w}[/itex] = 2[itex]\underline{i}[/itex] +b[itex]\underline{j}[/itex] - [itex]\underline{k}[/itex] and |[itex]\underline{v}[/itex]| = |[itex]\underline{w}[/itex]|, find the values of a and b so that [itex]\underline{v}[/itex] and [itex]\underline{w}[/itex] are perpendicular.

If v = ai+3j+3k and w = 2i+bj-k and |v| = |w|, find the values of a and b so that v and w are perpendicular.

Homework Equations



[itex]\underline{a}[/itex] - ([itex]\underline{a}[/itex].[itex]\underline{\hat{b}}[/itex])[itex]\underline{\hat{b}}[/itex]

The Attempt at a Solution


sqrt(a2+13) = sqrt(b2+5)

I am so confused right now. Any help would be great. Thanks
 
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  • #2
noahsdev said:

Homework Statement



If [itex]\underline{v}[/itex] = a[itex]\underline{i}[/itex] + 2[itex]\underline{j}[/itex] + 3[itex]\underline{k}[/itex] and [itex]\underline{w}[/itex] = 2[itex]\underline{i}[/itex] +b[itex]\underline{j}[/itex] - [itex]\underline{k}[/itex] and |[itex]\underline{v}[/itex]| = |[itex]\underline{w}[/itex]|, find the values of a and b so that [itex]\underline{v}[/itex] and [itex]\underline{w}[/itex] are perpendicular.


Homework Equations



[itex]\underline{a}[/itex] - ([itex]\underline{a}[/itex].[itex]\underline{\hat{b}}[/itex])[itex]\underline{\hat{b}}[/itex]

The Attempt at a Solution


sqrt(a2+13) = sqrt(b2+5)

I am so confused right now. Any help would be great. Thanks

That's one equation. To get another equation, use the requirement that u and v be perpendicular. Hint: There is a simple operation that can be used to determine whether two vectors are perpendicular.
 
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  • #3
Mark44 said:
That's one equation. To get another equation, use the requirement that u and v be perpendicular. Hint: There is a simple operation that can be used to determine whether two vectors are perpendicular.

Thanks, haha, so simple. I'm so angry at myself now. :)
 

1. What are perpendicular vectors?

Perpendicular vectors are two vectors that intersect at a right angle, or 90 degrees. This means that the dot product of these vectors is equal to 0.

2. How do you find the dot product of two vectors?

The dot product of two vectors is found by multiplying the corresponding components of the vectors and then adding them together. For example, if the vectors are [a, b] and [c, d], the dot product would be ac + bd.

3. What is the relationship between the dot product and perpendicularity?

The dot product of two vectors is equal to 0 if and only if the vectors are perpendicular. If the dot product is not equal to 0, then the vectors are not perpendicular.

4. How can I find the values of a and b for perpendicular vectors?

To find the values of a and b for perpendicular vectors, you can set up a system of equations using the dot product and the fact that the vectors are perpendicular. By solving this system of equations, you can find the values of a and b.

5. Are there any other methods for finding perpendicular vectors besides using the dot product?

Yes, there are other methods for finding perpendicular vectors. One method is to use the cross product, which results in a vector that is perpendicular to the original two vectors. Another method is to use the slope-intercept form of a line and the negative reciprocal of the slope to find the perpendicular vector.

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