If a,b are two vectors then prove that (a/|a|^2  -  b/|b|^2)^2 = (a-b)^2 / (|a|^2|b|^2)^2.

Asked by sunil2791 | 24th Nov, 2017, 07:30: PM

Expert Answer:

begin mathsize 16px style open parentheses straight a over open vertical bar straight a close vertical bar squared minus fraction numerator begin display style straight b end style over denominator begin display style open vertical bar straight b close vertical bar squared end style end fraction close parentheses squared
equals open parentheses fraction numerator straight a open vertical bar straight b close vertical bar squared minus straight b open vertical bar straight a close vertical bar squared over denominator open vertical bar straight a close vertical bar squared open vertical bar straight b close vertical bar squared end fraction close parentheses squared
equals open parentheses fraction numerator straight a squared open vertical bar straight b close vertical bar to the power of 4 minus 2 open vertical bar straight a close vertical bar squared open vertical bar straight b close vertical bar squared ab plus straight b squared open vertical bar straight a close vertical bar to the power of 4 over denominator open parentheses open vertical bar straight a close vertical bar squared open vertical bar straight b close vertical bar squared close parentheses squared end fraction close parentheses
take space open vertical bar straight a close vertical bar squared open vertical bar straight b close vertical bar squared common space from space numerator space ans space will space be space
fraction numerator open parentheses straight a minus straight b close parentheses squared over denominator open vertical bar straight a close vertical bar squared open vertical bar straight b close vertical bar squared end fraction end style

Answered by Arun | 26th Nov, 2017, 02:17: PM