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?

$\left( {{\rm{\vec P}} + {\rm{\vec Q}}} \right)$ is a unit vector along X-axis. If ${\rm{\vec P}} = \hat i - \hat j + \hat k,$ then what value is ${\rm{\vec Q}}?$

The adjacent sides of a parallelogram are represented by co-initial vectors $2\hat i + 3\hat j\,and\,\hat i + 4\hat j$. The area of the parallelogram is

If the magnitude of the sum of two vectors is equal to the magnitude of their difference, what is the angle between the two vectors?

Which of the following is not a property of the scalar product?

If the resultant of the vectors $\left( {\hat i + 2\hat j - \hat k} \right),\left( {\hat i - \hat j + 2\hat k} \right)$ and ${\rm{\vec C}}$ is a unit vector along the y-direction, then ${\rm{\vec C}}$ is

The sum of two vectors ${\rm{\vec A}}\,and\,{\rm{\vec B}}$ is at right angles to their difference. Then

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 ${{\rm{\vec B}}}$ ?

Two vectors $\vec{A}$ and $\vec{B}$ have magnitudes 3 and 4 units respectively, and their dot product is 6. What is the angle between them?

Two vectors $\vec{A}$ and $\vec{B}$ satisfy the condition $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$. Which of the following statements is true?

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