Let $\vec{a}$ and $\vec{b}$ be two non-zero vectors such that $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|$. Which of the following must be true?

Find the vector component of vector $\overrightarrow A = 2\widehat i + 3\widehat j$ along the direction of $\overrightarrow B = \widehat i + \widehat j$

If the magnitude of the sum of two vectors is equal to the magnitude of the difference of the two vectors, the angle between these vectors is:

Two vectors $\vec{A}$ and $\vec{B}$ satisfy the condition $|\vec{A} + \vec{B}|^2 = |\vec{A}|^2 + |\vec{B}|^2$. What is the angle between $\vec{A}$ and $\vec{B}$?

If $\overrightarrow P \,\,.\,\,\overrightarrow Q = 0\,and\,\overrightarrow P \,\, imes \,\,\overrightarrow Q = 0$, then the angle between $\overrightarrow Q \,and\,\overrightarrow R$ is

Dot product of two vectors $\overrightarrow A = \widehat i + 3\widehat j - 2\widehat k\,and\,\overrightarrow B = 3\widehat i - \widehat j + 4\widehat k$ is

If two vectors \vec{P} and \vec{Q} have equal magnitudes and their resultant also has the same magnitude, what is the angle between \vec{P} and \vec{Q}?

The X and Y components of vector ${\rm{\vec A}}$ have numerical values 6 and 6 respectively and that of $\left( {{\rm{\vec A}} + {\rm{\vec B}}} \right)$ have numerical values 10 and 9. What is the numerical value of ${{\rm{\vec B}}}$ ?

Velocity and acceleration vectors of a charged particle moving perpendicular to the direction of magnetic field at a given instant of time are $\overrightarrow V = 2\widehat i + c\widehat j\,and\,\overrightarrow a = 3\widehat i + 4\widehat j$ respectively. Then the value of ‘C’ is

If vector A = i + 2j - k and vector B = 3i - j + 2k, what is the value of A ⋅ B?

What is the numerical value of the vector $3\hat i + 4\hat j + 5\hat k?$