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

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LIST-I	LIST-II
A. $\vec{a}.\vec{c} + \vec{b}.\vec{c}$	I. $-25$
B. $\vec{a}.\vec{b} + \vec{a}.\vec{c}$	II. $-338$
C. $\vec{a}.\vec{b} + \vec{b}.\vec{c}$	III. $-169$
D. $2\left(\vec{a}.\vec{b} + \vec{b}.\vec{c} + \vec{c}.\vec{a}\right)$	IV. $-144$

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let $\vec{a}$ be a non-zero vector of magnitude '$a$' and $\lambda$ is a non-zero scalar, then $\lambda\vec{a}$ is a unit vector if

If $\theta$ is an acute angle and the vector $\vec{a} = (\sin \theta)\vec{i} + (\cos\theta)\vec{j}$ is perpendicular to the vector $\vec{b} = i - \sqrt{3}j$ then $\theta$ is equal to

If $\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$, then which of the following statements is/are correct?

(A) $\vec{a}$ and $\vec{b}$ are collinear

(B) $\vec{a}$ and $\vec{b}$ are perpendicular

(C) Angle between $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{4}$

(D) $|\vec{a} + \vec{b}| = 2\sqrt{5}$

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Which of the following statements are correct?

(A) $\hat{i} \times (\hat{j} \times \hat{k}) = \vec{0}$.

(B) If $|\vec{a}\times\vec{b}|=2$, $\vec{a}.\vec{b}=4$, then $|\vec{a}|^2|\vec{b}|^2=6$.

(C) The number of vectors of unit length perpendicular to $\vec{a}$ and $\vec{b}$ are 2.

(D) If $\vec{a}$ and $\vec{b}$ represent the diagonals of the rhombus, then $\vec{a}.\vec{b}=0$

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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

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