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CBSE Class 12-science Answered

verify that a x ( b + c) = ( a x b) + ( a x c)

  a = 4i – j + k b = i + j + k  c = i- j + k

a , b and c are vector         i j and k and k are unit vector

Asked by haroonrashidgkp | 01 Nov, 2018, 07:30: PM
Expert Answer
begin mathsize 16px style straight a with bar on top equals 4 straight i with hat on top minus straight j with hat on top plus straight k with hat on top comma space straight b with bar on top equals straight i with hat on top plus straight j with hat on top plus straight k with hat on top space and space straight c with bar on top equals straight i with hat on top minus straight j with hat on top plus straight k with hat on top
consider comma
straight a with bar on top cross times straight b with bar on top equals open parentheses 4 straight i with hat on top minus straight j with hat on top plus straight k with hat on top close parentheses cross times open parentheses straight i with hat on top plus straight j with hat on top plus straight k with hat on top close parentheses
space space space space space space space space space equals open vertical bar table row cell straight i with hat on top end cell cell straight j with hat on top end cell cell straight k with hat on top end cell row 4 cell negative 1 end cell 1 row 1 1 1 end table close vertical bar
space space space space space space space space space equals space left parenthesis negative 1 minus 1 right parenthesis straight i with hat on top minus open parentheses 4 minus 1 close parentheses straight j with hat on top plus open parentheses 4 plus 1 close parentheses straight k with hat on top
space space space space space space space space space equals negative 2 straight i with hat on top minus 3 straight j with hat on top plus 5 straight k with hat on top
Similarly space you space can space find space straight a with bar on top cross times straight c with bar on top
Also comma space space straight b with bar on top plus straight c with bar on top equals straight i with hat on top plus straight j with hat on top plus straight k with hat on top plus straight i with hat on top minus straight j with hat on top plus straight k with hat on top equals 2 straight i with hat on top plus 0 straight j with hat on top plus 2 straight k with hat on top
and space find space straight a with bar on top cross times open parentheses straight b with bar on top plus straight c with bar on top close parentheses space and space verify space straight a with bar on top cross times open parentheses straight b with bar on top plus straight c with bar on top close parentheses equals open parentheses straight a with bar on top cross times straight b with bar on top close parentheses plus straight a with bar on top cross times straight c with bar on top
end style
Answered by Sneha shidid | 02 Nov, 2018, 09:26: AM
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