91Ó°ÊÓ

In Exercises 35-38, find a unit vector orthogonal to both \(\vec{u}\) and \(\vec{v} .\) \(\vec{u}=\langle 1,1,1\rangle, \quad \vec{v}=\langle 2,0,1\rangle\)

How much work is performed in moving a box horizontally 10ft with a force of 20lb applied at an angle of \(10^{\circ}\) to the horizontal?

Find a unit vector orthogonal to both \(\vec{u}\) and \(\vec{v} .\) \(\vec{u}=\langle 1,-2,1\rangle, \quad \vec{v}=\langle 3,2,1\rangle\)

Find a unit vector orthogonal to both \(\vec{u}\) and \(\vec{v} .\) \(\vec{u}=\langle 5,0,2\rangle, \quad \vec{v}=\langle-3,0,7\rangle\)

Find a unit vector orthogonal to both \(\vec{u}\) and \(\vec{v} .\) \(\vec{u}=\langle 1,-2,1\rangle, \quad \vec{v}=\langle-2,4,-2\rangle\)

A bicycle rider applies \(150 \mathrm{lb}\) of force, straight down, onto a pedal that extends 7in horizontally from the crankshaft. Find the magnitude of the torque applied to the crankshaft.

How much work is performed in moving a box up the length of a 10 ft ramp that makes a \(5^{\circ}\) angle with the horizontal, with 50lb of force applied in the direction of the ramp?

A bicycle rider applies \(150 \mathrm{lb}\) of force, straight down, onto a pedal that extends 7in from the crankshaft, making a \(30^{\circ}\) angle with the horizontal. Find the magnitude of the torque applied to the crankshaft.

To turn a stubborn bolt, \(80 \mathrm{lb}\) of force is applied to a \(10 \mathrm{in}\) wrench. What is the maximum amount of torque that can be applied to the bolt?

To turn a stubborn bolt, \(80 \mathrm{lb}\) of force is applied to a \(10 \mathrm{in}\) wrench in a confined space, where the direction of applied force makes a \(10^{\circ}\) angle with the wrench. How much torque is subsequently applied to the wrench?