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 perpendicular is :

If $\vec a, \vec b$ and $\vec c$ are three vectors, then meaningless expressions are

(A) $\vec a.(\vec b\times\vec c)$

(B) $\vec a.(\vec b.\vec c)$

(C) $\vec a\times(\vec b\times\vec c)$

(D) $\vec a\times(\vec b.\vec c)$

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

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 :

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

If $\vec{a}$ is any vector, then $|\vec{a} \times \hat{i}|^2 + |\vec{a} \times \hat{j}|^2 + |\vec{a} \times \hat{k}|^2$ is equal to

Which of the following statements are correct ?

A. If $\vec{a}$ and $\vec{b}$ are two adjacent sides of a triangle, then the area of the triangle is $\frac{1}{2}|\vec{a}\times\vec{b}|$

B. If $\vec{a}$ and $\vec{b}$ are two adjacent sides of a triangle, then the area of the triangle is $\frac{1}{2}|\vec{a}.\vec{b}|$

C. If $\vec{a}$ and $\vec{b}$ are two adjacent sides of a parallelogram, then its area is $|\vec{a}\times\vec{b}|$

D. If $\vec{a}$ and $\vec{b}$ are two adjacent sides of a parallelogram, then its area is $|\vec{a}.\vec{b}|$

Choose the correct answer from the options given below: