Vectors

Lines and planes in 3D, scalar product tests, and shortest distance between skew lines.

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Q1Direct calculation6 marks
The line l1l_1 has equation r=i+j+λ(2i−j+k)\mathbf{r}=\mathbf{i}+\mathbf{j}+\lambda(2\mathbf{i}-\mathbf{j}+\mathbf{k}). The line l2l_2 has equation r=3i+2k+μ(i+j−k)\mathbf{r}=3\mathbf{i}+2\mathbf{k}+\mu(\mathbf{i}+\mathbf{j}-\mathbf{k}). Find the direction of the common perpendicular to l1l_1 and l2l_2.

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