The position vectors of three consecutive vertices of a parallelogram ABCD are A (4 i +2 j -6 k ), B (5 i -3 j + k ) and C (12 i +4 j +5 k ). The…

The position vectors of three consecutive vertices of a parallelogram ABCD are $\displaystyle \mathrm{A}(4 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}-6 \hat{\mathrm{k}}), \mathrm{B}(5 \hat{\mathrm{i}}-3 \hat{\mathrm{j}}+\hat{\mathrm{k}})$ and $\displaystyle \mathrm{C}(12 \hat{\mathrm{i}}+4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}})$. The position vector of $\displaystyle D$ is given by