Vector Addition – Analytical Method

Unspecified year 12 questions

1. If $\theta$ is the angle between two vectors, then the resultant vector is maximum, when value of $\theta$ is
2. If $\vec{A} = \hat{i} + \hat{j} + \hat{k}$ and $\vec{B} = 2\hat{i} - \hat{j} + 4\hat{k}$ then the unit vector along $\vec{A} + \vec{B}$ is
3. The sum of two vectors $\vec{A}$ and $\vec{B}$ is $\vec{C}$ such that $|\vec{C}| = |\vec{A}|$. The angle $\theta$ (in degrees) that the resultant of $2\vec{A}$ and $\vec{B}$ will make with $\vec{B}$ is
4. For which angle between two equal vectors $\vec{A}$ and $\vec{B}$ will the magnitude of the sum of two vectors be equal to the magnitude of each vector?
5. For two vectors A and B, $|A + B| = |A - B|$ is always true when
6. The position of particle is given by $\vec{r} = 2t^{2}\hat{i} + 3\hat{j} + 4\hat{k}$, where t is in second and the coefficients have proper units for $\vec{r}$ to be in metre. The $\vec{a}(t)$ of the particle at $t = 1 s$ is
7. A body moves in X - Y plane under the action of acceleration given by $\frac{1}{3}(6t\hat{i} + 4t\hat{j})$. Assuming that the body is at rest at time $t = 0$, the velocity of body at $t = 3\text{sec}$ is
8. A particle moves in the X - Y plane with a constant acceleration $1.5 m/s^{2}$ in the direction making an angle of $37^{\circ}$ with the X-axis. At $t = 0$ the particle is at the origin and its velocity is $8.0 m/s$ along the X-axis. Find the position of the particle at $t = 4.0 s$.
9. For motion in two or three dimensions, the angle between velocity and acceleration is
10. A particle moving with velocity $\vec{v} = k(y\hat{i} + x\hat{j})$, where k = constant. The general equation for its path is [C = constant ]
11. The coordinates of a particle moving in x - y plane at any instant of time t are $x = 4t^{2}$; $y = 3t^{2}$. The speed of the particle at that instant is
12. The shape of trajectory of the motion of an object is determined by