Two forces ${F_1} = 1\,N$ and ${F_2} = 2\,N$ act along the lines $x = 0$ and $y = 0$ respectively. Then the resultant of forces would be

A body is moving under the action of two forces ${\vec F_1} = 2\hat i - 5\hat j\,;\,{\vec F_2} = 3\hat i - 4\hat j$. Its velocity will become uniform under an additional third force ${\vec F_3}$ given by

Two vectors $\overrightarrow{{X}}$ and $\overrightarrow{{Y}}$ have equal magnitude. The magnitude of $(\overrightarrow{{X}}-\overrightarrow{{Y}})$ is ${n}$ times the magnitude of $(\overrightarrow{{X}}+\overrightarrow{{Y}})$. The angle between $\overrightarrow{{X}}$ and $\overrightarrow{{Y}}$ is -

Three forces given by vectors $2 \hat{i}+2 \hat{j}, 2 \hat{i}-2 \hat{j}$ and $-4 \hat{i}$ are acting together on a point object at rest. The object moves along the direction

The resultant of two vectors $A$ and $B$ is perpendicular to the vector $A$ and its magnitude is equal to half the magnitude of vector $B$. The angle between $A$ and $B$ is ....... $^o$