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Solve the following systems of equations:

Question:

If $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D}$ are the points with position vectors $\hat{i}+\hat{j}-\hat{k}, 2 \hat{i}-\hat{j}+3 \hat{k}$, $2 \hat{i}-3 \hat{k}, 3 \hat{i}-2 \hat{j}+\hat{k}$, respectively, find the projection of $\overrightarrow{\mathrm{AB}}$ along $\overrightarrow{\mathrm{CD}}$.

Solution:

We have,

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