Question:
Let $\overrightarrow{\mathrm{a}}=4 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}-\hat{\mathrm{k}}, \overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}-4 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}$ and $\overrightarrow{\mathrm{c}}=3 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\hat{\mathrm{k}}$
Find a vector $\overrightarrow{\mathrm{d}}$ which is perpendicular to both $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$, and is such that $\overrightarrow{\mathrm{d}} \cdot \overrightarrow{\mathrm{c}}=21$.
Solution:
