The dot products of a vector with the vector

Question:

The dot products of a vector with the vector $(\hat{\mathrm{i}}+\hat{\mathrm{j}}-3 \hat{\mathrm{k}}),(\hat{\mathrm{i}}+3 \hat{\mathrm{j}}-2 \hat{\mathrm{k}})$ and $(2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+4 \hat{\mathrm{k}})$ are 0,5 and 8 respectively. Find the vector.

Solution:

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