Question

For the following three vectors, what is 3C·(2A x B )?

A. 2.00 + 3.00 - 7.00
B. -3.00 + 3.00 + 2.00
C. 6.00 - 8.00

Answer 1

2 A x B = ( 2*(2 i + 3 j - 7 k ) x ( - 3 i + 3 j + 2 k ) ) =
= ( 4 i + 6 j - 14 k ) x ( - 3 i + 3 j + 2 k ) =
i j k i j
= | 4 6 -14 | 4 6
-3 3 2 -3 3
= 12 i + 42 j + 12 k - 8 j + 42 i + 18 k = 54 i + 34 j + 30 k
3 C * ( 2 A x B ) = 3 ( 6 i - 8 j + 0 k ) * ( 54 i + 34 j + 30 k ) =
= ( 18 i - 24 j + 0 k ) * ( 54 i + 34 j + 30 k ) =
= ( 18 * 54 ) j - ( 24 * 34 k ) + ( 0 * 30 ) k = 972 i - 816 j