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If a and b are two non-zero, non-collinear vectors, then 2[abhati]hati+2[abhatj]hatj+2[abhatk]hatk+[abc] is equal to |
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Answer» `2(axxb)` Now , `[abhat(i)]=|{:(a_1,a_2,a_3),(b_1,b_2,b_3),(1,0,0):}|` `=a_(1)(0-0)-a_2(0-b_3)+a_(3)(0-b_2)=a_2b_3-a_3b_2` `therefore 2[ab hat(i)]hat(i)=2(a_2b_3-a_3b_2)hat(i)` Similarly, `2[a b hat(j)]hat(j)=2(a_1b_2-a_1b_3)hat(j)` and `2[a BHAT(k)]hat(k)=2(a_2b_2-a_2b_1)hat(k)` `therefore 2[ab hat(i)]hat(i)+2[abhat(j)]hat(j)+2[abhat(k)]hat(k)+[aba]` `=2[(a_2b_3-a_(3)b_2)hat(i)+(a_3b_1-a_1b_3)hat(j)+0+(a_1b_2-a_2b_1)hat(k)]` `=2(axxb)` . |
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