Match List - I with List - II.

	List - I		List - II
(A)	Area of triangle $\Delta$ with adjacent sides $\vec{a}$ and $\vec{b}$	(I)	$\vec{a} \times \vec{b}$
(B)	Area of parallelogram with adjacent sides $\vec{a}$ and $\vec{b}$	(II)	$\frac{1}{2}\lvert \vec{a} \times \vec{b} \rvert$
(C)	$(\vec{a} - \vec{b}) \times (\vec{a} + \vec{b})$	(III)	$\lvert \vec{a} \times \vec{b} \rvert$
(D)	$\lvert \vec{a} \rvert \lvert \vec{b} \rvert \sin\theta \hat{n}$, where symbols have their usual meaning	(IV)	$2(\vec{a} \times \vec{b})$

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If $\vec{a}, \vec{b}$ and $\vec{c}$ are three unit vectors such that $\vec{a} + 2\vec{b} - 3\vec{c} = \vec{0}$, then the value of $2\vec{a}.\vec{b} - 6\vec{b}.\vec{c} - 3\vec{c}.\vec{a}$ is

If $\vec{a},\vec{b}$ and $\vec{c}$ are three vectors such that $\lvert \vec{a} \rvert=\frac{1}{\sqrt{2}}$, $\lvert \vec{b} \rvert=\frac{1}{\sqrt{3}}$, $\lvert \vec{c} \rvert=\frac{1}{\sqrt{6}}$, $\lvert \vec{a}+\vec{b}+\vec{c} \rvert=1$ and $\vec{c}=\lambda(\vec{a}\times\vec{b})$. The angle between $\vec{a}$ and $\vec{b}$ is

If $|\vec{a} - \vec{r}| = |\vec{a}| = |\vec{r}| = 1$, then angle between $\vec{a}$ and $\vec{r}$ is

If $\vec{a}$ and $\vec{b}$ are two non-zero vectors such that $|\vec{a}\times\vec{b}|^2 + |\vec{a}.\vec{b}|^2 = 100$ and $|\vec{a}| = 5$ then the value of $|\vec{b}|$ is

If $\vec a, \vec b$ and $\vec c$ are vectors such that $|\vec a|=5, |\vec b|=12, |\vec c|=13$ and $\vec a+\vec b+\vec c=\vec 0$, then

Match List-I with List-II

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Match List-I with List-II

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