If $|\vec a|=2, |\vec b|=7, \vec a \times \vec b = 3\hat i + 2\hat j + 6\hat k$, then the angle between $\vec a$ and $\vec b$ is equal to

Arrange the vectors in descending order of their magnitudes.

(A) $\hat{i} + \hat{j} + \hat{k}$

(B) $2\hat{i} - 3\hat{j}$

(C) $\frac{1}{2}\hat{i} - \frac{1}{3}\hat{j}$

(D) $2\hat{i} - \hat{k}$

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The projection vector of the vector $2\hat{i} + 3\hat{j} + \hat{k}$ on $2\hat{i} + \hat{j} - 2\hat{k}$ is

Let $\vec{OA} = 2\hat{i} - \hat{j} + \hat{k}$ and $\vec{OB} = \hat{i} + \hat{j} - \hat{k}$. Then

A. The magnitude of vector $\vec{OA}$ is 6

B. The magnitude of vector $\vec{OB}$ is $\sqrt{3}$

C. The vector $\vec{AB}$ is $(-\hat{i} + 2\hat{j} - 2\hat{k})$

D. $\vec{OA} \cdot \vec{OB} = 0$

E. $\vec{OA} \parallel \vec{OB}$

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Vector projection of $7\hat i+\hat j+4\hat k$ on the vector $2\hat i+6\hat j-3\hat k$ is

If $\vec a=2\hat i-3\hat j+\hat k, \vec b=-\hat i+\hat k, \vec c=2\hat j-\hat k$ are three vectors, then area of the parallelogram having diagonals $(\vec a+\vec b)$ and $(\vec b+\vec c)$ 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

Choose the correct answer from the options given below :