જો $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ અને $\vec{b}=\hat{i}+2\hat{j}+3\hat{k}$ હોય,તો $(\vec{a}+\vec{b})$ અને $(\vec{a}-\vec{b})$ બંનેને લંબ હોય તેવો એકમ સદિશ શોધો.

• A
  $\frac{-1}{\sqrt{6}}\hat{i} + \frac{2}{\sqrt{6}}\hat{j} - \frac{1}{\sqrt{6}}\hat{k}$
• B
  $\frac{1}{\sqrt{6}}\hat{i} - \frac{2}{\sqrt{6}}\hat{j} + \frac{1}{\sqrt{6}}\hat{k}$
• C
  $\frac{-1}{\sqrt{6}}\hat{i} - \frac{2}{\sqrt{6}}\hat{j} + \frac{1}{\sqrt{6}}\hat{k}$
• D
  $\frac{1}{\sqrt{6}}\hat{i} + \frac{2}{\sqrt{6}}\hat{j} + \frac{1}{\sqrt{6}}\hat{k}$