If $\vec{A}$ and $\vec{B}$ are two non-zero vectors such that $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$, which of the following must be true?

If vectors $\overrightarrow A$ and $\overrightarrow B$ are $3\widehat i - 4\widehat j + 5\widehat k$ and $2\widehat i + 3\widehat j - 4\widehat k$ respectively, then find the unit vector parallel to $\overrightarrow A + \overrightarrow B$

If ${\rm{\vec A}}\,and\,\overrightarrow B$ denote the sides of a parallelogram and its area is $\frac{1}{2}AB$(A and B are the magnitude of ${\rm{\vec A}}\,and\,\overrightarrow B$ respectively), the angle between ${\rm{\vec A}}\,and\,\overrightarrow B$ is

What is the unit vector along $\hat i + \hat j\,\,?$

If ${\rm{\vec A}}\,and\,\overrightarrow B$ denote the sides of a parallelogram and its area is $\frac{1}{2}AB$(A and B are the magnitude of ${\rm{\vec A}}\,and\,\overrightarrow B$ respectively), the angle between ${\rm{\vec A}}\,and\,\overrightarrow B$ is

What is the unit vector along $\hat i + \hat j\,\,?$

Given $heta$ is the angle between ${\rm{\vec A}}\,and\,{\rm{\vec B}}$. Then $\left| {\hat A imes \hat B\;} \right|$ is equal to

Given $heta$ is the angle between ${\rm{\vec A}}\,and\,{\rm{\vec B}}$. Then $\left| {\hat A imes \hat B\;} \right|$ is equal to

Given ${\rm{\vec A}} = 4\hat i + 6\hat j\,and\,{\rm{\vec B}} = 2\hat i + 3\hat j$. Which of the following is correct?

Which of the following quantities is a scalar?

Given ${\rm{\vec c}} = {\rm{\vec a}} imes {\rm{\vec b}}$. The angle which ${\rm{\vec a}}$ makes with ${\rm{\vec c}}$ is