Advertisement Remove all ads

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

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
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×