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11TH · MATH

Question 7

menu_bookSolutionmenu_bookTheorymenu_book•(i)u×(−u)=0\mathbf{u} \times (-\mathbf{u}) = 0u×(−u)=0menu_book•(ii)u×v=−v×u\mathbf{u} \times \mathbf{v} = -\mathbf{v} \times \mathbf{u}u×v=−v×umenu_book•(iii)u×(kv)=(ku)×v=k(u×v)\mathbf{u} \times (k\mathbf{v}) = (k\mathbf{u}) \times \mathbf{v} = k(\mathbf{u} \times \mathbf{v})u×(kv)=(ku)×v=k(u×v)menu_book•(iv)u×(v+w)=(u×v)+(u×w)\mathbf{u} \times (\mathbf{v} + \mathbf{w}) = (\mathbf{u} \times \mathbf{v}) + (\mathbf{u} \times \mathbf{w})u×(v+w)=(u×v)+(u×w)
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11TH · MATH

Question 7

menu_bookSolutionmenu_bookTheorymenu_book•(i)u×(−u)=0\mathbf{u} \times (-\mathbf{u}) = 0u×(−u)=0menu_book•(ii)u×v=−v×u\mathbf{u} \times \mathbf{v} = -\mathbf{v} \times \mathbf{u}u×v=−v×umenu_book•(iii)u×(kv)=(ku)×v=k(u×v)\mathbf{u} \times (k\mathbf{v}) = (k\mathbf{u}) \times \mathbf{v} = k(\mathbf{u} \times \mathbf{v})u×(kv)=(ku)×v=k(u×v)menu_book•(iv)u×(v+w)=(u×v)+(u×w)\mathbf{u} \times (\mathbf{v} + \mathbf{w}) = (\mathbf{u} \times \mathbf{v}) + (\mathbf{u} \times \mathbf{w})u×(v+w)=(u×v)+(u×w)
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