**Problem Statement:**A particle is located at the position vector \( \vec{r} = (6.00 \hat{\imath} + 7.00 \hat{\jmath}) \) m and a force exerted on it is given by \( \vec{F} = (4.00 \hat{\imath} + 3.00 \hat{\jmath}) \) N.(a) What is the torque acting on the particle about the origin?\[ \tau = \text{______} \, \text{N} \cdot \text{m} \]**Explanation:**Here, we need to calculate the torque (\( \tau \)) acting on the particle about the origin. Torque is given by the cross-product of the position vector (\( \vec{r} \)) and the force vector (\( \vec{F} \)).To find the torque \( \tau \):\[ \tau = \vec{r} \times \vec{F} \] \[ \vec{r} = (6.00 \hat{\imath} + 7.00 \hat{\jmath}) \, \text{m} \]\[ \vec{F} = (4.00 \hat{\imath} + 3.00 \hat{\jmath}) \, \text{N} \]The torque \( \vec{\tau} \) is computed as:\[ \vec{\tau} = (6.00 \hat{\imath} + 7.00 \hat{\jmath}) \times (4.00 \hat{\imath} + 3.00 \hat{\jmath}) \]Solve the cross product to find the magnitude and direction.---This transcribed text can be used in educational resources to provide students practice in vector cross product and understanding torque. **Instruction (f): Determine the Position Vector**For this task, you are required to determine the position vector of a point located on the y-axis. **Vector Representation:**- The vector is represented as **\(\vec{r} = \_\_\_\_\_\_ \, \text{m}\)**. - You need to specify the vector's value within the provided box to denote the position on the y-axis.The position vector typically has the format \(\vec{r} = (x, y, z)\). Since the point is on the y-axis, x and z components would be zero, resulting in a vector of the form \((0, y, 0)\). Specify a value for \(y\) based on the context to complete the answer.

F→ = 4 i ⏜+ 3 j⏜r⏜ = 6 i⏜ + 7 j ⏜F→ = 4 i ⏜+ 3 j⏜r⏜ = 6 i⏜ + 7 j ⏜ The torque is give by τ→ = r→ x F→τ→ =6 i⏜ + 7 j ⏜ x 4 i ⏜+ 3 j⏜τ→ = 18 k⏜ - 28 k⏜ = - 10 k ⏜ Nm

Answered: A particle is located at the position…

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A particle is located at the position vector r = (6.00î + 7.0oj) m and a force exerted on it is given by F = (4.00î + 3.00j) N. (a) What is the torque acting on the particle about the origin? N.m

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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