The unit vector in the direction of the sum of vectors $\vec{a} = 2\hat{i} + 2\hat{j} - 5\hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} + 3\hat{k}$ is :

Let $\vec{a} = 4\hat{i} - \hat{j} + 3\hat{k}$ and $\vec{b} = -2\hat{i} + \hat{j} - 2\hat{k}$. Then

(A) $\vec{a}$ is a unit vector

(B) $\vec{a} \times \vec{b} = -\hat{i} + 2\hat{j} + 2\hat{k}$

(C) $\vec{a}$ and $\vec{b}$ are parallel vectors

(D) $\vec{a}$ and $\vec{b}$ are neither parallel nor perpendicular vectors

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If $|\vec{a}| = 10$, $|\vec{b}| = 2$ and $\vec{a} \cdot \vec{b} = 12$, then value of $|\vec{a} \times \vec{b}|$ is :

Let $\vec{a}$ and $\vec{b}$ be any two vectors such that $\vec{a} = 2\hat{i} + \hat{j} + 3\hat{k}$ and $\vec{b} = 3\hat{i} + 5\hat{j} - 2\hat{k}$ then

Match the LIST-I with LIST-II

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Let $\vec{a},\vec{b},\vec{c}$ are three vectors such that $|\vec{a}|=3, |\vec{b}|=2, |\vec{c}|=1$. If the projection of $\vec{b}$ along $\vec{c}$ is equal to the projection of $\vec{a}$ along $\vec{c}$ and $\vec{b} \perp \vec{a}$ , then the value of $|2\vec{a}-2\vec{b}+3\vec{c}|$ is equal to

Match the LIST-I with LIST-II

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A unit vector perpendicular to the vectors $\hat{i} - \hat{j}$ and $\hat{i} + \hat{j}$ is