The torque of force F⃗=(2 î-3 ĵ+4 k̂) newton acting at the point r⃗=(3 î+2 ĵ+3 k̂) metre about o

step 1 In this question we will learn about some basic concept of the units and dimensions. The questio

The torque of force F⃗=(2 î-3 ĵ+4 k̂) newton acting at the...

The torque of force $\vec{F}=(2 \hat{i}-3 \hat{j}+4 \hat{k})$ newton acting at the point $\vec{r}=(3 \hat{i}+2 \hat{j}+3 \hat{k})$ metre about origin is (in $\mathrm{N}-\mathrm{m}$ ) (A) $6 \hat{i}-6 \hat{j}+12 \hat{k}$ (B) $17 \hat{i}-6 \hat{j}-13 \hat{k}$ (C) $-6 \hat{i}+6 \hat{j}-12 \hat{k}$ (D) $-17 \hat{i}+6 \hat{j}+13 \hat{k}$

The torque of force $\vec{F}=(2 \hat{i}-3 \hat{j}+4 \hat{k})$ newton acting at the point $\vec{r}=(3 \hat{i}+2 \hat{j}+3 \hat{k})$ metre about origin is (in $\mathrm{N}-\mathrm{m}$ )
(A) $6 \hat{i}-6 \hat{j}+12 \hat{k}$
(B) $17 \hat{i}-6 \hat{j}-13 \hat{k}$
(C) $-6 \hat{i}+6 \hat{j}-12 \hat{k}$
(D) $-17 \hat{i}+6 \hat{j}+13 \hat{k}$

Key Concepts

Torque

Torque is a measure of the rotational effect produced by a force acting at a distance from a pivot point. It is defined as the cross product of the position vector (from the pivot to the point of application of the force) and the force vector. The magnitude of torque depends on the magnitudes of the force and the position vector as well as the sine of the angle between them, which shows how effectively the force causes rotation.

Cross Product

The cross product is a binary operation on two vectors in three-dimensional space that results in a third vector, which is perpendicular to the plane containing the original vectors. It is used in various physics applications to calculate quantities such as torque and angular momentum, and it incorporates the directional aspect provided by the right-hand rule.

Determinant Method

The determinant method is a systematic approach to compute the cross product of two vectors by arranging the vectors into a 3x3 matrix with unit vectors in the first row. Calculating the determinant of this matrix provides the components of the resulting vector. This method is widely used because it simplifies the computation and organizes the process clearly.

Right-Hand Rule

The right-hand rule is a convention used to determine the direction of the vector resulting from a cross product. By pointing the index finger in the direction of the first vector and the middle finger in the direction of the second, the thumb naturally points in the direction of the resulting vector. This rule ensures consistency in defining the orientation of vector operations such as torque.

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