Find the magnitude of the torque of a couple | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the position vectors of the points be $\vec{r}_1 = \hat{i} - \hat{j} + \hat{k}$ and $\vec{r}_2 = 2\hat{i} - 3\hat{j} - \hat{k}$.The force $\ve

Vedclass · Accepted Answer

$5\sqrt{5}$

Vedclass · Answer

(C) Let the position vectors of the points be $\vec{r}_1 = \hat{i} - \hat{j} + \hat{k}$ and $\vec{r}_2 = 2\hat{i} - 3\hat{j} - \hat{k}$.The force $\vec{F} = 3\hat{i} + 2\hat{j} - \hat{k}$ acts at $\vec{r}_1$ and $-\vec{F}$ acts at $\vec{r}_2$.The torque $\vec{	au}$ of the couple is given by $\vec{	au} = \vec{r} 	imes \vec{F}$,where $\vec{r} = \vec{r}_1 - \vec{r}_2$.$\vec{r} = (\hat{i} - \hat{j} + \hat{k}) - (2\hat{i} - 3\hat{j} - \hat{k}) = -\hat{i} + 2\hat{j} + 2\hat{k}$.$\vec{	au} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ -1 & 2 & 2 \ 3 & 2 & -1 \end{vmatrix} = \hat{i}(-2 - 4) - \hat{j}(1 - 6) + \hat{k}(-2 - 6) = -6\hat{i} + 5\hat{j} - 8\hat{k}$.The magnitude of the torque is $|\vec{	au}| = \sqrt{(-6)^2 + 5^2 + (-8)^2} = \sqrt{36 + 25 + 64} = \sqrt{125} = 5\sqrt{5}$.

Find the magnitude of the torque of a couple formed by a force $\vec{F} = 3\hat{i} + 2\hat{j} - \hat{k}$ acting at the point $\hat{i} - \hat{j} + \hat{k}$ and the force $-\vec{F}$ acting at the point $2\hat{i} - 3\hat{j} - \hat{k}$.

Similar Questions

$\vec{a}, \vec{b}, \vec{c}$ are three vectors each having $\sqrt{2}$ magnitude such that $(\vec{a}, \vec{b})=(\vec{b}, \vec{c})=(\vec{c}, \vec{a})=\frac{\pi}{3}$. If $\vec{x}=\vec{a} \times(\vec{b} \times \vec{c})$ and $\vec{y}=\vec{b} \times(\vec{c} \times \vec{a})$,then

The adjacent sides of a parallelogram are $\vec{a} = 3\hat{i} + \hat{j} + 4\hat{k}$ and $\vec{b} = \hat{i} - \hat{j} + \hat{k}$. Then,the area of the parallelogram is . . . . . . sq. units.

If $\bar{a}=\hat{j}-\hat{k}$ and $\bar{c}=\hat{i}-\hat{j}-\hat{k}$,then the vector $\bar{b}$ satisfying $\bar{a} \times \bar{b}+\bar{c}=\vec{0}$ and $\bar{a} \cdot \bar{b}=3$ is

If $a, b, c, d$ are coplanar vectors,then $(a \times b) \times (c \times d)$ is equal to

If $2\vec{a} + 3\vec{b} + \vec{c} = \vec{0}$,then $\vec{a} \times \vec{b} + \vec{b} \times \vec{c} + \vec{c} \times \vec{a}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module