In $\triangle ABC$ :

(A) $\vec{AB} + \vec{BC} + \vec{CA} = \vec{O}$

(B) $\vec{AB} + \vec{BC} - \vec{AC} = \vec{O}$

(C) $\vec{AB} + \vec{BC} - \vec{CA} = \vec{O}$

(D) $\vec{AB} - \vec{CB} + \vec{CA} = \vec{O}$

(E) $\vec{AB} - \vec{CB} - \vec{CA} = \vec{O}$

Choose the correct answer from the options given below :

If $|\vec{a}| = 3$ and $|\vec{b}| = 4$, then a value of $\lambda$ for which $\vec{a} + \lambda\vec{b}$ and $\vec{a} - \lambda\vec{b}$ are perpendiculars is.

A vector of magnitude 9, which is perpendicular to both the vectors $4\hat{i}-\hat{j}+3\hat{k}$ and $-2\hat{i}+\hat{j}-2\hat{k}$ is:

If $\vec{a}$ and $\vec{b}$ are two collinear vectors, then which of the following statements is/are incorrect?

(A) $\vec{b} = \lambda\vec{a}$, for some scalar $\lambda$.

(B) Always $\vec{a} = \pm\vec{b}$.

(C) the respective components of $\vec{a}$ and $\vec{b}$ are proportional.

(D) both vectors $\vec{a}$ and $\vec{b}$ always have same direction.

Choose the correct answer from the options given below:

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 A (3, 2), B (1, -1) and C (2, 1) are three vertices of a parallelograms ABCD, then its area (in sq.units) is equal to

If $\theta$ is the acute angle between two unit vectors $\vec{a}$ and $\vec{b}$, then $\cos\frac{\theta}{2} =$