Assertion : Let a =2 i +3 j - k , b =4 i +6 j -2 k , then a b = o Reason : If a o , b o…

Assertion : Let \(\vec{a}=2 \hat{i}+3 \hat{j}-\hat{k}, \vec{b}=4 \hat{i}+6 \hat{j}-2 \hat{k},\) then \(\vec{a} \times \vec{b}=\vec{o}\)
Reason : If \(\overrightarrow{\mathrm{a}} \neq \overrightarrow{\mathrm{o}}\), \(\overrightarrow{\mathrm{b}} \neq \overrightarrow{\mathrm{o}}\) and \(\stackrel{\rightharpoonup}{\mathrm{a}}\) and \(\overrightarrow{\mathrm{b}}\) are non–collinear vectors, then \(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}\)= ab sin θ \(\hat{\mathrm{n}}\), where θ is the smaller angle between the vectors \(\stackrel{\rightharpoonup}{\mathrm{a}}\)and \(\overrightarrow{\mathrm{b}}\) and \(\hat{\mathrm{n}}\) is unit vector such that \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{~b}}, \hat{\mathrm{n}}\)taken in this order form right handed orientation