The vector $\{(a^2+a-2)\hat{i}+(a^2-4)\hat{j}-(a^2-5a+6)\hat{k}\}$ makes acute angles with coordinate axes, then values of $a$ lies in :

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

If $\vec{a}, \vec{b}, \vec{c}$ are three vectors such that $|\vec{a}| = 2, |\vec{b}| = 5, |\vec{c}| = 3$ and $\vec{a} + 2\vec{b} - 3\vec{c} = \vec{0}$, then angle between $\vec{b}$ and $\vec{c}$ is equal to:

For the vectors $\vec a=\hat i-2\hat j+3\hat k$ and $\vec b=3\hat i-2\hat j+\hat k$, Which of the following are correct?

(A) $|\vec a|=14$

(B) $|\vec a|=|\vec b|$

(C) $\vec a . \vec b=10$

(D) angle between $\vec a$ and $\vec b$ is $\cos^{-1}\left(\dfrac{5}{7}\right)$

Choose the correct answer from the options given below:

If $\vec{a}$ and $\vec{b}$ are two non-zero vectors such that $|\vec{a} \cdot \vec{b}| = |\vec{a} \times \vec{b}|$, then the angle $\theta$ between $\vec{a}$ and $\vec{b}$ is

If $|\vec{a}| = 5$, $|\vec{b}| = 6$ and $\vec{a}.\vec{b} = 18$, then value of $|\vec{a} \times \vec{b}|$ is

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 :