For any two non zero vectors $\vec{a}$ and $\vec{b}$

A. If $|\vec{a}|=|\vec{b}|$ then $\vec{a}=\vec{b}$

B. If $\vec{a}=\vec{b}$ then $|\vec{a}|=|\vec{b}|$

C. $\vec{a}.\vec{b}=\vec{b}.\vec{a}$

D. $\vec{a}×\vec{b}=\vec{b}×\vec{a}$

E.  Area of the Parallelogram $=\frac{1}{2}|\vec{a}×\vec{b}|$, where $\vec{a}$ and $\vec{b}$ represent the diagonals of the parallelogram.

Choose the correct answer from the options given below :

B, C, E only

The correct answer is Option (1) → B, C, E only

(A) false as $\vec a= \vec b$ only if $|\vec a|=|\vec b|$ and $\hat a = \hat b$

(B) Equal vectors must have equal magnitudes and directions. So this is true.

(C) True (dot product is commutative)

(D) False (cross product is not commutative)

(E) True, This is because in a parallelogram, the diagonals bisect each other, and the cross product of the diagonals gives twice the area of the parallelogram formed by the original adjacent sides.  

⇒ B, C, E only true