The force vec{F} = 7hat{i} + 3hat{j} - 5hat{k | vedclass

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

Question

(A) Given:Position vector $\vec{r} = \hat{i} - \hat{j} + \hat{k}$Force vector $\vec{F} = 7\hat{i} + 3\hat{j} - 5\hat{k}$Torque $\vec{	au}$ is defined

Vedclass · Accepted Answer

$2\hat{i} + 12\hat{j} + 10\hat{k}$

Vedclass · Answer

(A) Given:Position vector $\vec{r} = \hat{i} - \hat{j} + \hat{k}$Force vector $\vec{F} = 7\hat{i} + 3\hat{j} - 5\hat{k}$Torque $\vec{	au}$ is defined as the cross product of position vector and force vector:$\vec{	au} = \vec{r} 	imes \vec{F}$Calculating the cross product using the determinant method:$\vec{	au} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & -1 & 1 \ 7 & 3 & -5 \end{vmatrix}$Expanding the determinant:$\vec{	au} = \hat{i}((-1)(-5) - (1)(3)) - \hat{j}((1)(-5) - (1)(7)) + \hat{k}((1)(3) - (-1)(7))$$\vec{	au} = \hat{i}(5 - 3) - \hat{j}(-5 - 7) + \hat{k}(3 + 7)$$\vec{	au} = 2\hat{i} - \hat{j}(-12) + 10\hat{k}$$\vec{	au} = 2\hat{i} + 12\hat{j} + 10\hat{k}$

The force $\vec{F} = 7\hat{i} + 3\hat{j} - 5\hat{k}$ acts on a particle whose position vector is $\vec{r} = \hat{i} - \hat{j} + \hat{k}$. What is the torque of the given force about the origin?

Similar Questions

$A$ tap can be easily opened or closed with the help of two fingers because:

Why is the handle of a door or window placed at the end opposite to the hinged side?

The moment of the force,$\overrightarrow{F} = 4\hat{i} + 5\hat{j} - 6\hat{k}$ at point $(2, 0, -3)$,about the point $(2, -2, -2)$,is given by

The coordinates of a particle with respect to origin in a given reference frame is $(1, 1, 1) \ m$. If a force of $\vec{F} = \hat{i} - \hat{j} + \hat{k} \ N$ acts on the particle,then the magnitude of the torque (with respect to origin) in the $z$-direction is . . . . . . .

Three forces $F, 2F$ and $3F$ act on a rod $AB$ which is pivoted at $A$. The anticlockwise moments of forces $F, 2F$ and $3F$ about the pivot $A$ are respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module