Consider the polar coordinates x = r cos 0 and y = r sin 0. Or...

    

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Consider the polar coordinates x = r cos 0 and y = r sin 0. Or (a) Show that Or y = cos 0, x = sin 0, x cos 0 = and ly 00 sin = . (b) Show that =-sin 0 i + cos 0 j. 3 +0100 = cos 0i+sin0j and (c) Using the chain rule, show that V = (d) If A = A, + A , show that V. A = (rAr) + Ae, since = 0 and 30 follows from part b. Consider the polar coordinates x = r cos 0 and y = r sin 0. Or (a) Show that Or y = cos 0, x = sin 0, x cos 0 = and ly 00 sin = . (b) Show that =-sin 0 i + cos 0 j. 3 +0100 = cos 0i+sin0j and (c) Using the chain rule, show that V = (d) If A = A, + A , show that V. A = (rAr) + Ae, since = 0 and 30 follows from part b.