Question

If $\vec{a}\times(\hat{i}-\hat{j}+\hat{k})=(\hat{i}-\hat{j}+\hat{k})\times\vec{b}$ and $|\vec{a}+\vec{b}|=3\sqrt{3}$, then the possible values of $(\vec{a}+\vec{b})\cdot(3\hat{i}+2\hat{j}+\hat{k})$ are

• A. $\pm 1$
• B. $\pm 2$
• C. $\pm 4$
• D. $\pm 6$
• E. $\pm 8$

Hint:

Logic Tip: Rearranging cross products to equal $\vec{0}$ is a fundamental trick in vector algebra to prove collinearity/parallelism. Whenever you see $\vec{A} \times \vec{C} = \vec{C} \times \vec{B}$, immediately deduce that $(\vec{A}+\vec{B})$ is parallel to $\vec{C}$.

Answer 1

The Correct Option is D