Finding the Value of a Vertical Vector

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Homework Help Overview

The problem involves determining the value(s) of t for which the vector <3t² - t³, 2t²> is vertical, focusing on the conditions that define a vertical vector in a coordinate system.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants explore the definition of a vertical vector, questioning the implications of its x-component being zero. There is discussion about setting the x-component equal to zero to find the appropriate value(s) of t.

Discussion Status

The discussion is active, with participants providing insights into the characteristics of vertical vectors and confirming the approach of setting the x-component to zero as a valid method to find t.

Contextual Notes

Participants are considering the implications of the vector's orientation and the mathematical relationships involved, with some uncertainty about the initial steps taken in the problem-solving process.

Loppyfoot
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Homework Statement


For what value(s) of t is <3t2-t3, 2t2> a vertical vector?

The Attempt at a Solution


I set them equal to each other, and received t=1. Is that what I am supposed to do?
 
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Well think about it. If a vector is vertical, what do we know about its x component?
 
Would it be coming off of it at a right angle? Could I use the Pythagorean Theorem?
 
If a vector is vertical, meaning it points straight up along the y-axis in standard position, its x-component will have to be zero, or else it will not point exactly straight up.
 
Ok, so should I set:
3t2-t3= 0?
Then solve for t?
 
Yes. Doing so should give you the correct answer.
 

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