a x (b x c)= (a * c)b - (a * b)c
where * means the dot product
2007-08-27 19:21:08 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
BXC= i.................j............... k
....... b1.............. b2............b3
........ c1................c2............. c3
= i(b2c3-b3c2) -j(b1c3- b3c1) +k(b1c2-b2c1)
Ax(BxC)= ..... i................... j ................... k
..... ....... .....a1.................. a2................a3
....... .... (b2c3-b3c2)...... -(b1c3- b3c1) ....(b1c2-b2c1)
= i(a2b1c2-a2b2c1+a3b1c3-a3b3c1)
-j(a1b1c2-a1b2c1-a3b2c3+a3b3c2)
+k(-a1b1c3+a1b3c1-a2b2c3+a2b3c2)
NOW L.H.S.
(a1c1+a2c2+a3c3)(b1i+b2j+b3j)-(a1b1+a2b2+a3b3)(c1i+c2j+c3k)
= i(a2b1c2-a2b2c1+a3b1c3-a3b3c1)
-j(a1b1c2-a1b2c1-a3b2c3+a3b3c2)
+k(-a1b1c3+a1b3c1-a2b2c3+a2b3c2) =R.H.S. qed
2007-08-28 06:23:23 · answer #1 · answered by mramahmedmram 3 · 0⤊ 0⤋
Replace all the vectors with their components.
For instance let vector a be
Then perform the operations (x and * ) as you would normally do on these vectors.
2007-08-27 19:44:52 · answer #2 · answered by Demiurge42 7 · 0⤊ 0⤋