Question

Problem 2 (5 pt.) Show that: where the velocity show that and the dot denotes the time derivative. Extra credit: Using (1) and (2), = Hints: r2 = F-, r = (r2)1/2

Answer 1

A (B time C) A^rightarrow = a_1 j^^+ a_2 j^^+ a_3 k^^B^rightarrow = b_1 i^^+ b_2 j^^+ b_3 k^^C^rightarrow = c_1 i^^+ c_2 j^^+ c_3 k^^A^rightarrow (B^rightarrow times C^rightarrow) Vertical-bar i b_1 c_1 j b_2 c_2 k b_3 c_3 Vertical-bar = Vertical-bar a_1 b_1 c_1 a_2 b_2 c_2 a_3 b_3 c_3 Vertical-bar From the property of determinant, if any two rows are interchanged the value will remain same Vertical-bar a_1 b_1 c_1 a_2 b_2 c_2 a_3 b_3 c_3 Vertical-bar = Vertical-bar b_1 c_1 a_1 b_2 c_2 a_2 b_3 c_3 a_3 b_3 c_3 a_3 Vertical-bar = Vertical-bar c_1 a_1 b_1 c_2 a_2 b_2 c_3 a_3 b_3 Vertical-bar A^rightarrow (B^rightarrow times C^rightarrow) = B^rightarrow (C^rightarrow times A^rightarrow) = C^rightarrow (A^rightarrow times B^rightarrow) \r\n part b A times B times C = A^rightarrow times [i b_1 c_1 j b_2 c_2 k b_3 c_3] D^rightarrow = A^rightarrow times ((b_2 c_3 - c_2 b_3) i + (b_3 c_1 - b_1 c_3) j + (b_1 c_2 - c_1 b_2) k) = Vertical-bar i a_1 b_2 c_3 - c_2 b_3 j a_2 b_3 c_1 - b_1 c_3 k a_3 b_1 c_2 - c_1 b_2 Vertical-bar