# A unit vector co planar with $\overrightarrow {i}+\overrightarrow {j}+ 3\overrightarrow {k}$ and $\overrightarrow {i} +3 \overrightarrow {j}+ \overrightarrow {k}$ and perpendicular to $\overrightarrow {i}+ \overrightarrow {j}+ \overrightarrow {k}$ is

$(a)\;\frac{1}{\sqrt 2}(j+k) \quad (b)\;\frac{1}{\sqrt 3}(\overrightarrow{i}-\overrightarrow{j}+ \overrightarrow{k}) \quad (c)\;\frac{1}{\sqrt 2}(\overrightarrow {j}- \overrightarrow{k}) \quad (d)\;\frac{1}{\sqrt 3}(\overrightarrow{i}+ \overrightarrow{j}-\overrightarrow{k})$

$(c)\;\frac{1}{\sqrt 2}(\overrightarrow {j}- \overrightarrow{k})$
answered Nov 7, 2013 by