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First question:

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This first question is kind of weird. I'm not even sure where to go with it. If anyone has a hint, that would be awesome.

From [itex] \vec A \times \vec B = -\vec B \times \vec A [/itex] deduce [itex] \vec A \times \vec A = 0 [/itex]

Can it be as simple as:

let [tex] \vec B = \vec A_0 | \vec A_0 = \vec A [/tex]

thus: [tex] \vec A \times \vec A_0 = -\vec A_0 \times \vec A = 0 [/tex]

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Second question:

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Find the minimum and maximum speed if [itex] x=t+\cos t [/itex], [itex]y=t-\sin t [/itex].

Please allow me to take advantage of the inner space operator for sake of ease while writing the vectors :)

Thus:

[tex] \vec x = <t+\cos t,t-\sin t> [/tex]

[tex] \vec v = <1-\sin t, 1-cos t> [/tex]

So speed is computed as: [itex] |\vec v| [/itex]. Therefore the largest speed values that can occur are when: [itex] \vec v = <1,2> or <2,1> [/itex] and the lowest speed values that can occur are when [itex] \vec v = <1,0> or <0,1> [/itex].

Is this reasoning even correct with this problem?

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# Homework Help: Two Questions - calculus

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