Curvature=|r'(t)xr''(t)|/|r'(t)|^3Find Curvature of r(t)=t*i+(1/2)t^2*j+t^2*k

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The discussion focuses on finding the curvature of the vector function r(t) = t*i + (1/2)t^2*j + t^2*k. The derivatives r'(t) and r''(t) are calculated as r'(t) = <1, t, 2t> and r''(t) = <0, 1, 2>, respectively. A cross product of these derivatives is attempted, resulting in r'(t) x r''(t) = <0, t, 4t>. However, it is noted that the cross product calculation is incorrect, indicating a need for clarification on the specific question being asked. The discussion emphasizes the importance of correctly computing the cross product to proceed with finding the curvature.
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Homework Statement


Find the curvature of r(t)=t*i+(1/2)t^2*j+t^2*k.

Homework Equations


None.

The Attempt at a Solution


r'(t)=<1, t, 2t>
r"(t)=<0, 1, 2>
r'(t)xr''(t)=<0, t, 4t>
 
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Math10 said:

Homework Statement


Find the curvature of r(t)=t*i+(1/2)t^2*j+t^2*k.

Homework Equations


None.

The Attempt at a Solution


r'(t)=<1, t, 2t>
r"(t)=<0, 1, 2>
r'(t)xr''(t)=<0, t, 4t>

You should really state what your question is, but the cross product is wrong.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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