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Question Number 54420 by gunawan last updated on 03/Feb/19

$$\mathrm{Let}\mathbf{a}=\mathbf{i}+\mathbf{j}\mathrm{and}\mathbf{b}=2\mathbf{i}-\mathbf{k},\mathrm{the}\mathrm{point}\mathrm{of}$$$$\mathrm{intersection}\mathrm{of}\mathrm{the}\mathrm{lines}\mathbf{r}\times \mathbf{a}=\mathbf{b}\times \mathbf{a}$$$$\mathrm{and}\mathbf{r}\times \mathbf{b}=\mathbf{a}\times \mathbf{b}\mathrm{is}$$

Answered by tanmay.chaudhury50@gmail.com last updated on 03/Feb/19

$$r=ix+jy+kz$$$$\mathit{r}\times \mathit{a}=\left[ijk\right]=i(0-z)-j(0-z)+k(x-y)$$$$\left[xyz\right]$$$$\left[110\right]$$$$\mathit{b}\times \mathit{a}=\left[\mathit{i}\mathit{j}\mathit{k}\right]=\mathit{i}(0+1)-\mathit{j}(0+1)+\mathit{k}\left(2\right)$$$$[20-1]$$$$\left[110\right]$$$$\mathit{s}\mathit{o}(-\mathit{z})=1(-\mathit{z})=1\mathit{x}-\mathit{y}=2[\mathit{z}=-1]]$$$$\mathit{r}\times \mathit{b}=\left[\mathit{i}\mathit{j}\mathit{k}\right]=\mathit{i}(-\mathit{y}-0)-\mathit{j}(-\mathit{x}-2\mathit{z})+\mathit{k}(0-2\mathit{y})$$$$\left[\mathit{x}\mathit{y}\mathit{z}\right]$$$$[20-1]$$$$\mathit{a}\times \mathit{b}=-\left(\mathit{b}\times \mathit{a}\right)=-\mathit{i}+\mathit{j}-2\mathit{k}$$$$\mathit{s}\mathit{o}-\mathit{y}=-1[\mathit{y}=1]$$$$\mathit{x}+2\mathit{z}=1\mathit{x}=1-2(-1)=3$$$$$$$$\mathit{x}-\mathit{y}=2\mathit{x}=2+1=3[\mathit{x}=3\mathit{y}=1\mathit{z}=-1]$$$$\mathit{r}=3\mathit{i}+\mathit{j}-\mathit{k}$$$$\mathit{p}\mathit{l}\mathit{s}\mathit{w}\mathit{r}\mathit{i}\mathit{t}\mathit{e}\mathit{q}\mathit{u}\mathit{e}\mathit{s}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{c}\mathit{l}\mathit{e}\mathit{a}\mathit{r}\mathit{l}\mathit{y}....$$$$$$$$$$

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