Question

express the component of a cross product vector C= A x B in terms of Levi civita product vector and the component of a and B, using this relation show that A . ( AxB ) = 0

Answer 1

write a dimesions of each room as a single unit a 10' 3" * 16' 9"

Answer 2

Ck = eijk Ai Bj
e = 0 if any indices the same
e = 1 if order is 123, 231 etc
e = -1 if order is 132, 213 etc
so
A dot C = Ak Ck = Ak eijk Ai Bj
well for example. look at A1 C1
A1 C1 = A1 eij1 Ai Bj
= A1 A2 B3 - A1 A3 B2
now A2 C2 = A2 A3 B1 -A2 A1 B3
then A3 C3 = A3 A1 B2 - A3 A2 B1
When we add
For every PLUS we have an equal Negative
for example
A1 A2 B3 [- A1 A3 B2 ]
A2 C2 = A2 A3 B1 -A2 A1 B3
A3 C3 = [ A3 A1 B2 ] - A3 A2 B1

Answer 3

10' = 120 inches + 3 = 123 inches
16' = 192 inches + 9 = 201 inches

Answer 4

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