What is the torque of the force 𝐅=(2 𝐢-3 𝐢̂+4 𝐤̂) N acting at the point 𝐫=(3 𝐢̂+2 𝐣̂+3 𝐤̂) m abo

step 1 As we know that as we know that tau is equal to R multiplication F, which is equal to 3i cap plu

What is the torque of the force 𝐅=(2 𝐢-3 𝐢̂+4 𝐤̂) N acting...

What is the torque of the force $\mathbf{F}=(2 \mathbf{i}-3 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}) \mathrm{N}$ acting at the point $\mathbf{r}=(3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \mathrm{m}$ about the origin? (a) $-17 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+13 \hat{\mathrm{k}}$ (b) $-6 \hat{i}+6 \hat{j}-12 \hat{k}$ (c) $17 \hat{\mathbf{i}}-6 \hat{\mathbf{j}}-13 \hat{\mathbf{k}}$ (d) $6 \hat{i}-6 \hat{j}+12 \hat{k}$

What is the torque of the force $\mathbf{F}=(2 \mathbf{i}-3 \hat{\mathbf{i}}+4 \hat{\mathbf{k}}) \mathrm{N}$
acting at the point $\mathbf{r}=(3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}) \mathrm{m}$ about the
origin?
(a) $-17 \hat{\mathrm{i}}+6 \hat{\mathrm{j}}+13 \hat{\mathrm{k}}$
(b) $-6 \hat{i}+6 \hat{j}-12 \hat{k}$
(c) $17 \hat{\mathbf{i}}-6 \hat{\mathbf{j}}-13 \hat{\mathbf{k}}$
(d) $6 \hat{i}-6 \hat{j}+12 \hat{k}$

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Key Concepts

Torque

Torque is a physical quantity that measures the tendency of a force to rotate an object about an axis, pivot, or fulcrum. It is calculated as the cross product of the position vector (which defines the point of application relative to the pivot) and the force vector, capturing both the magnitude of the force and its lever arm relative to the pivot.

Cross Product

The cross product is a vector operation used in three-dimensional space that takes two vectors and produces a third vector perpendicular to the plane formed by the original vectors. Its magnitude is given by the product of the magnitudes of the original vectors and the sine of the angle between them, and it is essential for computing rotational effects in physics.

Vector Representation

Vectors represent quantities having both magnitude and direction and are central in describing physical phenomena in mechanics. In problems involving torque, vectors are used to denote both the point of application of a force (position vector) and the force itself, with operations like the cross product enabling the calculation of rotational effects.

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