Find a unit vector perpendicular to each of the vector \( \overrightarrow a + \overrightarrow b\) and \( \overrightarrow a - \overrightarrow b\), where \( \overrightarrow a = \hat i + \hat j + \hat k\) and \( \overrightarrow b = \hat i + 2\hat j +3\hat k\)

Question

$(a)\;\pm\large\frac{-2\hat i+4\hat j-2\hat k}{\sqrt{24}}\qquad(b)\;\pm\large\frac{2\hat i+4\hat j+2\hat k}{\sqrt{24}}\qquad(c)\;\pm\large\frac{-2\hat i-4\hat j-2\hat k}{\sqrt{24}}\qquad(d)\;\pm\large\frac{2\hat i+4\hat j-2\hat k}{24}$