Let F––(t)=2ti–−5j–+t2k––𝐹_(𝑡)=2𝑡𝑖_−5𝑗_+𝑡2𝑘_ and G––(t)=(1−t)i–+1tk––𝐺_(𝑡)=(1−𝑡)𝑖_+1𝑡𝑘_ where t∈R+𝑡∈𝑅+.
Question
Let F––(t)=2ti–−5j–+t2k––𝐹_(𝑡)=2𝑡𝑖_−5𝑗_+𝑡2𝑘_ and G––(t)=(1−t)i–+1tk––𝐺_(𝑡)=(1−𝑡)𝑖_+1𝑡𝑘_ where t∈R+𝑡∈𝑅+.
Solution
I'm sorry, but you didn't ask a specific question about the functions F(t) and G(t). Could you please clarify what you want to know? For example, are you interested in their derivatives, integrals, or something else?
Similar Questions
Let F––(t)=t2i–+tj–+k––𝐹_(𝑡)=𝑡2𝑖_+𝑡𝑗_+𝑘_ and G––(t)=i–+tj–+t2k––𝐺_(𝑡)=𝑖_+𝑡𝑗_+𝑡2𝑘_ be two vector functions defined for each t∈R𝑡∈𝑅.
Let F––(t)=t2i–+tj–+k––𝐹_(𝑡)=𝑡2𝑖_+𝑡𝑗_+𝑘_ and G––(t)=i–+tj–+t2k––𝐺_(𝑡)=𝑖_+𝑡𝑗_+𝑡2𝑘_ be two vector functions defined for each t∈R𝑡∈𝑅. (a) The derivative of F––(t)×G––(t)𝐹_(𝑡)×𝐺_(𝑡) with respect to t𝑡, at t=1𝑡=1 is given by
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