Finding the Value of a Vertical Vector

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To determine when the vector <3t² - t³, 2t²> is vertical, the x-component must equal zero. Setting 3t² - t³ = 0 allows for solving for t. This results in the equation t²(3 - t) = 0, leading to t = 0 or t = 3 as the values for which the vector is vertical. The discussion emphasizes that a vertical vector has no horizontal component, confirming the need for the x-component to be zero. Thus, the correct values of t for a vertical vector are 0 and 3.
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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