If $\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}$ and $\vec{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}$ are two non zero vectors inclined at an angle $\theta$, then identify the correct option out of the given options. (a) $\cos \theta=\frac{\vec{a} \cdot \vec{b}}{|\vec{a}| \cdot|\vec{b}|}$ Choose the most appropriate answer from the options given below |
(a), (b) and (d) only (a), (b) and (e) only (b), (d) and (e) only (a) and (b) only |
(a), (b) and (d) only |
(a) → correct (b) → correct (c) → incorrect for perpendicularity $a_1b_1+a_2b_2+a_3b_3=0$ (d) → $\theta=\pi$ $\vec{a} \times \vec{b}=|\vec{a}| . |\vec{b}| \sin \pi \hat{n}$ $=0$ → correct (e) → incorrect as $\sin \theta = \frac{|\vec{a} × \vec{b}|}{|\vec{a}|. |\vec{b}|}$ Option: 1 |