If $\vec{A} = 3\hat{i} + 4\hat{j}$ and $\vec{B} = 6\hat{i} + 8\hat{j}$,where $A$ and $B$ are the magnitudes of vectors $\vec{A}$ and $\vec{B}$ respectively,which of the following is incorrect?

The resultant of two vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ is $\overrightarrow{R}$. If $\overrightarrow{Q}$ is doubled,the new resultant is perpendicular to $\overrightarrow{P}$. Then $R$ equals

Given $\vec{A} + \vec{B} + \vec{C} = \vec{0}$. The magnitudes of two vectors are equal,and the magnitude of the third vector is $\sqrt{2}$ times that of the other two. What are the angles between the vectors?

$A$ vector $\vec{A}$ having magnitude $6$ units is added to vector $\vec{B}$,which is along the $x$-axis. The resultant of $\vec{A}$ and $\vec{B}$ is along the $y$-axis. If the magnitude of the resultant of $\vec{A}$ and $\vec{B}$ is three times that of $\vec{B}$,then the magnitude of $\vec{B}$ is:

Two particles are located at an equal distance from the origin. The position vectors of these are represented by $\overrightarrow{A} = 2\hat{i} + 3n\hat{j} + 2\hat{k}$ and $\overrightarrow{B} = 2\hat{i} - 2\hat{j} + 4p\hat{k}$,respectively. If both vectors are at a right angle to each other,the value of $n^{-1}$ is . . . . . . .

The maximum and minimum magnitude of the resultant of two given vectors are $17$ units and $7$ units respectively. If these two vectors are at right angles to each other,the magnitude of their resultant is