Vector A=2ti+tj-t^3k and B=sinti+costj evaluate
A..d/dt(A.B)
B..d/dt(A.A)
C..d/dt(A×B)
D..show that d/dt(A×A) is equal to zero.
A.
"\\dfrac{d}{dt}(A\\cdot B)=2\\sin t+2t\\cos t+\\cos t-t\\sin t"
B.
"\\dfrac{d}{dt}(A\\cdot A)=10t"
C.
"=i(0+t^3\\cos t)-j(0+t^3\\sin t)+k(2t\\cos t-t\\sin t)"
"\\dfrac{d}{dt}(A\\times B)=(3t^2\\cos t-t^3\\sin t)i-(3t^2\\sin t+t^3\\cos t)j"
"+(2\\cos t-2t\\sin t-\\sin t-t\\cos t)k"
D.
"=i(-t^4+t^4)-j(-2t^4+2t^4)+k(2t^2-2t^2)=0"
"\\dfrac{d}{dt}(A\\times A)=0"
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