The Vector Product of Vectors

If momentum of a particle is given by $\overrightarrow{p}=10\sin \left(2t\right)\hat{\mathrm{i}}+10\cos \left(2t\right)\hat{\mathrm{j}}$

a) Find the magnitude of force at any time.

b) Find the angle between momentum and force.

The angle between $\overrightarrow{A}-\overrightarrow{B}$ and $\overrightarrow{A}\times \overrightarrow{B}$ is $\left(\overrightarrow{A}\ne \overrightarrow{B}\right)$:

What is cross product?

Which of the following is not true about vectors $\overrightarrow{A},\overrightarrow{B}$ and $\overrightarrow{C}$?

Find $\overrightarrow{a}·\overrightarrow{b}$ and $\overrightarrow{a}\times \overrightarrow{b}$ if $\overrightarrow{a}=\hat{\mathrm{i}}+2\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\left|\overrightarrow{b}\right|=3$ acting along $\overrightarrow{c}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$.

The linear velocity of a rotating body is given by $\overrightarrow{v}=\overrightarrow{\omega }\times \overrightarrow{r}\text{ where }\overrightarrow{\omega }$ is the angular velocity and $\overrightarrow{r}$ is the radius vector. The angular velocity of body $\overrightarrow{\omega }=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}$ and this radius vector $\overrightarrow{r}=4\hat{\mathrm{j}}-3 \hat{\mathrm{k}}$, then $\left|\overrightarrow{v}\right|$ is

Given that $\overrightarrow{a}\text{ and }\overrightarrow{b}$ are two non-zero vectors, then the value of $\left(\overrightarrow{a}+\overrightarrow{b}\right)\times \left(\overrightarrow{a}-\overrightarrow{b}\right)$ is,

The angle between two vectors $\overrightarrow{a}\text{ and }\overrightarrow{b}\text{ is }\pi /2$. Then $\left|\hat{a}\times \hat{b}\right|$

If $\left|\overrightarrow{a}\times \overrightarrow{b}\right|=a b$ then the angle between $\overrightarrow{a}\text{ and }\overrightarrow{b}$ is 

Prove that $\left(\overrightarrow{A}+\overrightarrow{B}\right)\times \left(\overrightarrow{A}-\overrightarrow{B}\right)=2 \left(\overrightarrow{B}\times \overrightarrow{A}\right)$

Find the cross product  $\overrightarrow{r}\times \overrightarrow{F}$ .Given $\overrightarrow{ F} = \hat{i} + \hat{j}+ \hat{k}$and $\overrightarrow{r}$is the distance between two points whose coordinates are (-2, 3, 4) and (1, 2, 3).

If $\overrightarrow{A}= 5 \hat{i} -3 \hat{j} + 4\hat{k}$ and $B = \hat{j}-\hat{k},$  find the sine of the angle between $\overrightarrow{A}$ and $\overrightarrow{B}$.

The vector $\overrightarrow{F}$ is a force of$3.0$ newton making an angle of $60°$ with the displacement $\overrightarrow{R}$ of magnitude $4.0 m$. Find

(b) The magnitude and direction of the cross product $\overrightarrow{R} \times \overrightarrow{F}$ .

What are the values of the following : 

$\left(i\right) \overrightarrow{B}\times \overrightarrow{A }, if \overrightarrow{A}\times \overrightarrow{B}=\overrightarrow{C}$

What are the values of the following : 

$\left(i\right) \overrightarrow{A}\times \overrightarrow{A}$

Obtain the condition for the two vectors $\overrightarrow{A}=x_1 \widehat{i }+y_1 \hat{j}+z_1 \hat{k} , \overrightarrow{B}=x_2 \widehat{i }+y_2 \hat{j}+z_2 \hat{k}$ to be parallel. ?

What is the angle between $\overrightarrow{a} \times \overrightarrow{b}$and $\overrightarrow{b} \times \overrightarrow{a}$?

What is the condition under which the magnitude of cross product is equal to the dot product ?

What is the condition for parallelism of two vectors ?

If $\overrightarrow{A}\times \overrightarrow{B}=0$ under the condition $\overrightarrow{A}\ne 0,\overrightarrow{ B}\ne 0$ .What is the angle between them ?