11. Vector/ Cross Product: 10 Find the cross product B A C for the following vec

Question

11. Vector/ Cross Product: 10 Find the cross product B A C for the following vectors (a) A = (2.0i-40-k) m and C = (3.0i + 4.0j + 10.0k) N; (b) A = (3.0i + 4.0j + 10.0 k) m and C = (201-4.0^ + k) N; (c) A = (-3.0i-4.0J) m and C = (-30i + 4.0) N; and (d) A =-9.0 mi and C = (-201 + 3.0+ 2.0 k) N. ^ ^ Between the four parts, use at least three different met hods for computing the cross product. The options indlude the two equations on the Equation Sheet, the" mnemonic' demonstrated in class, and the determinant met hod using matrix notation. Using the“ mnemonic" demonstrated in dass, where in the diagram, I insert the actual num- bers (and units) of A (b) (middle row) and C(b) (bottom row). If we had left it symbol- ically, we would have derived Equation (33) of part (a). I'll follow the plus-red (upper-left to lower-right) and minus-blue (lower-left to upper-right) pattern explicitly. 3m 4m

Explanation / Answer

a) A X C = [ i j k ]

[ 2 -4 1]

[ 3 4 10]

i (-40 - 4) - j (20-3) + k(8 + 12)

= -44i -17j +20k

b) [ i j k ]

[ 3 4 10]

[ 2 -4 1]

= i(4 + 44) - j(3-20) + k(-12-8)

= 44i +17j -20k

c) [ i j k ]

[ -3 -4 0]

[ -3 4 0]

= i(0 -0 ) - j(0-0) + k(-12-12)

= -24k

d) [ i j k ]

[ 0 -9 0]

[ -2 3 2]

= i(-18 - 0) - j(0 - 0) + k(0 - 18)

= -18i -18k

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