There are two force vectors,one of $5\, N$ and the other of $12\, N$. At what angle should the two vectors be added to get a resultant vector of $17\, N$,$7\, N$,and $13\, N$ respectively?

Let $\overrightarrow C = \overrightarrow A + \overrightarrow B$. Which of the following statements are correct?
$(A)$ It is possible to have $|\overrightarrow C| < |\overrightarrow A|$ and $|\overrightarrow C| < |\overrightarrow B|$.
$(B)$ $|\overrightarrow C|$ is always greater than $|\overrightarrow A|$.
$(C)$ $|\overrightarrow C|$ may be equal to $|\overrightarrow A| + |\overrightarrow B|$.
$(D)$ $|\overrightarrow C|$ is never equal to $|\overrightarrow A| + |\overrightarrow B|$.

Two forces of magnitudes $3 \, N$ and $4 \, N$ are acting on an object. If the angle between them is $90^\circ$,then their resultant force is ... $N$.

The magnitude of the vector sum of two forces $10 \ N$ and $6 \ N$ cannot be ......... $N$.

Which vector must be added to the resultant vector $\vec{P} = 2\hat{i} + 7\hat{j} - 10\hat{k}$ and $\vec{Q} = \hat{i} + 2\hat{j} + 3\hat{k}$ to obtain a unit vector along the $X$-axis?

The resultant of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$. If the magnitude of $\vec{B}$ is doubled,the new resultant vector becomes perpendicular to $\vec{A}$. Then the magnitude of $\vec{C}$ is