Vector Addition — Prelims Questions

Two forces, $F_1 = 10,\text{N}$ and $F_2 = 10,\text{N}$, act on a particle. If the angle between them is $60^circ$, what is the magnitude of the resultant force?

A vector $\vec{A}$ has components $A_x = 3$ units and $A_y = 4$ units. Another vector $\vec{B}$ has components $B_x = -1$ unit and $B_y = 2$ units. What is the magnitude of the resultant vector $\vec{R} = \vec{A} + \vec{B}$?

Which of the following statements about vector addition is INCORRECT?

A boat is moving with a velocity of $8,\text{m/s}$ in still water. If it crosses a river of width $100,\text{m}$ flowing at $6,\text{m/s}$ due East, and the boatman steers the boat perpendicular to the river flow, what is the resultant velocity of the boat relative to the ground?

Three forces act on a particle: $\vec{F}_1 = 3\hat{i} + 4\hat{j},\text{N}$, $\vec{F}_2 = -2\hat{i} + 2\hat{j},\text{N}$, and $\vec{F}_3 = -1\hat{i} - 6\hat{j},\text{N}$. What is the resultant force acting on the particle?

Given two vectors $\vec{P}$ and $\vec{Q}$. If $|\vec{P} + \vec{Q}| = |\vec{P} - \vec{Q}|$, what is the angle between vectors $\vec{P}$ and $\vec{Q}$?

A particle is displaced by $3,\text{m}$ towards East and then by $4,\text{m}$ towards North. The total distance covered and the magnitude of the resultant displacement are respectively: