Vectors Questions

If a vector 2î + 3ĵ + 8 is perpendicular to the vector 4ĵ - 4î + α, then the value of α is :

If a vector 2î + 3ĵ + 8 is perpendicular to the vector 4ĵ - 4î + α , then the value of α is :

If the angle between the vectors

A particle starting from the origin $(0,0)$ moves in a straight line in the $(x,y)$ plane. Its coordinates at a later time are $(\sqrt{3},3)$. The path of the particle makes with the $x$ -axis an angle of:

$\vec{A}$ and $\vec{B}$ are two vectors and $\theta$ is the angle between them, if $|\vec{A}\times \vec{B}|=\sqrt{3}(\vec{A}\cdot \vec{B})$, the value of $\theta$ is:

If $\vec{F}$ is the force acting on a particle having position vector $\vec{r}$ and $\vec{\tau }$ be the torque of this force about the origin, then:

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

A particle has initial velocity $(2\hat{i}+3\hat{j})$ and acceleration $(0.3\hat{i}+0.2\hat{j})$. The magnitude of velocity after $10$ seconds will be:

If vectors $\vec{A}=\cos \omega t\hat{i}+\sin \omega t\hat{j}$ and $\vec{B}=\cos \frac{\omega t}{2}\hat{i}+\sin \frac{\omega t}{2}\hat{j}$ are functions of time, then the value of $t$ at which they are orthogonal to each other is:

If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is: