A force F⃗=(2 1̂+3 ĵ-k̂) N is acting on a body at a position 𝐫=(6 𝐢̂+3 𝐣̂-2 𝐤̂). The torque abou

step 1 In this question, we have given a force vector that is acting on a body and we have given the po

A force F⃗=(2 1̂+3 ĵ-k̂) N is acting on a body at a position...

A force $\vec{F}=(2 \hat{1}+3 \hat{j}-\hat{k}) N$ is acting on a body at a position $\overrightarrow{\mathbf{r}}=(6 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})$. The torque about the origin is: (a) $(3 \hat{i}+2 \hat{j}+12 \hat{k}) \mathrm{Nm}$ (b) $(9 \hat{1}+\hat{j}+7 \hat{k}) \mathrm{Nm}$ (c) $(\hat{1}+2 \hat{j}+12$ k $) \mathrm{Nm}$ (d) $(3 \hat{i}+12 \hat{j}+\hat{k}) \mathrm{Nm}$

A force $\vec{F}=(2 \hat{1}+3 \hat{j}-\hat{k}) N$ is acting on a body at a position $\overrightarrow{\mathbf{r}}=(6 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})$. The torque about the origin
is:
(a) $(3 \hat{i}+2 \hat{j}+12 \hat{k}) \mathrm{Nm}$
(b) $(9 \hat{1}+\hat{j}+7 \hat{k}) \mathrm{Nm}$
(c) $(\hat{1}+2 \hat{j}+12$ k $) \mathrm{Nm}$
(d) $(3 \hat{i}+12 \hat{j}+\hat{k}) \mathrm{Nm}$

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Key Concepts

Torque

Torque is a measure of the tendency of a force to cause an object to rotate about a pivot or axis. It is defined as the cross product of the position vector (which defines the point of application of the force relative to the pivot) and the force vector. The magnitude of the torque depends on both the magnitude of the force and its perpendicular distance from the axis of rotation.

Cross Product

The cross product is a binary operation on two vectors in three-dimensional space that results in another vector which is perpendicular to the plane containing the two original vectors. Its magnitude equals the product of the magnitudes of the two vectors and the sine of the angle between them, and it plays a critical role in calculating torque.

Vector Representation of Physical Quantities

In mechanics, forces and positions are often represented as vectors to capture both their magnitudes and directions. This vector representation allows for the systematic analysis of their interactions, such as the computation of torque using vector operations like the cross product.

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