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11TH · MATH

Question 6

menu_bookSolutionmenu_bookTheorymenu_book•(a) Find the value of: (i)2i×2j⋅k2\mathbf{i} \times 2\mathbf{j} \cdot \mathbf{k}2i×2j⋅k(ii) $3\mathbf{j} \cdot (\mathbf{k} \times \mathbf{i})$ (iii) $[\mathbf{k}\,\mathbf{i}\,\mathbf{j}]$ (iv) $[\mathbf{i}\,\mathbf{i}\,\mathbf{k}]$menu_book•(b) Prove thatu⋅(v×w)+v⋅(w×u)+w⋅(u×v)=3u⋅(v×w)\mathbf{u} \cdot (\mathbf{v} \times \mathbf{w}) + \mathbf{v} \cdot (\mathbf{w} \times \mathbf{u}) + \mathbf{w} \cdot (\mathbf{u} \times \mathbf{v}) = 3\mathbf{u} \cdot (\mathbf{v} \times \mathbf{w})u⋅(v×w)+v⋅(w×u)+w⋅(u×v)=3u⋅(v×w)
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11TH · MATH

Question 6

menu_bookSolutionmenu_bookTheorymenu_book•(a) Find the value of: (i)2i×2j⋅k2\mathbf{i} \times 2\mathbf{j} \cdot \mathbf{k}2i×2j⋅k(ii) $3\mathbf{j} \cdot (\mathbf{k} \times \mathbf{i})$ (iii) $[\mathbf{k}\,\mathbf{i}\,\mathbf{j}]$ (iv) $[\mathbf{i}\,\mathbf{i}\,\mathbf{k}]$menu_book•(b) Prove thatu⋅(v×w)+v⋅(w×u)+w⋅(u×v)=3u⋅(v×w)\mathbf{u} \cdot (\mathbf{v} \times \mathbf{w}) + \mathbf{v} \cdot (\mathbf{w} \times \mathbf{u}) + \mathbf{w} \cdot (\mathbf{u} \times \mathbf{v}) = 3\mathbf{u} \cdot (\mathbf{v} \times \mathbf{w})u⋅(v×w)+v⋅(w×u)+w⋅(u×v)=3u⋅(v×w)
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