Question

Let $\vec{a} = 2\hat{i} - 2\hat{j} + 4\hat{k}$, $\vec{b} = -5\hat{i} - \hat{j} + 8\hat{k}$ and $\vec{c} = 3\hat{i} + \hat{j} - \lambda \hat{k}$. If $\vec{a} + \vec{b} + \vec{c}$ and $\vec{a} - \vec{b} + \vec{c}$ are perpendicular, then the values of $\lambda$ are:

• A. $4$ and $-12$
• B. $-2$ and $12$
• C. $-6$ and $14$
• D. $-3$ and $12$
• E. $-4$ and $12$

Hint:

Perpendicular vectors $\Rightarrow$ dot product equals zero.

Answer 1

Answer: (E)