Advertisement Remove all ads

Prove that abcabc[a¯ b¯+c¯ a¯+b¯+c¯]=0 - Mathematics and Statistics

Advertisement Remove all ads
Advertisement Remove all ads
Sum

Prove that `[bar"a"  bar"b" + bar"c"  bar"a" + bar"b" + bar"c"] = 0`

Advertisement Remove all ads

Solution

`[bar"a"  bar"b" + bar"c"  bar"a" + bar"b" + bar"c"]`

`= bar"a" . [(bar"b" + bar"c") xx (bar"a" + bar"b" + bar"c")]`

`= bar"a" . (bar"b" xx bar"a" + bar"b" xx bar"b" + bar"b" xx bar"c" + bar"c" xx bar"a" + bar"c" xx bar"b" + bar"c" xx bar"c")`

`= bar"a" . (bar"b" xx bar"a") + bar"a" (bar"b" xx bar"b") + bar"a".(bar"b" xx bar"c") + bar"a" . (bar"c" xx bar"a") + bar"a" . (bar"c" xx bar"b") + bar"a" . (bar"c" xx bar"c")`

`= 0 + 0 + bar"a" . (bar"b" xx bar"c") + 0 - bar"a". (bar"b" xx bar"c") + 0`

= 0

Concept: Vector Triple Product
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×