The magnitude of the vector resulting from the addition of two vectors,$6\hat{i} + 7\hat{j}$ and $3\hat{i} + 4\hat{j}$,is:

If the magnitudes of vectors $\vec P$,$\vec Q$,and $\vec R$ are $5$,$12$,and $13$ units respectively,and if $\vec P + \vec Q = \vec R$,then the angle between $\vec Q$ and $\vec R$ is:

Six vectors,$\overrightarrow a$ through $\overrightarrow f$,have the magnitudes and directions indicated in the figure. Which of the following statements is true?

Let the two forces have equal magnitude $A$. If the magnitude of the resultant is $\frac{2A}{3}$,then the angle between those two forces is:

Three vectors are expressed as $\vec{a} = 4\hat{i} - \hat{j}$,$\vec{b} = -3\hat{i} + 2\hat{j}$,and $\vec{c} = -\hat{k}$. The unit vector along the direction of the sum of these vectors is:

If the angle between two vectors $A$ and $B$ is $120^{\circ}$,then their resultant $C$ will be: