Mathematics I / Cross Product and Geometry in Space
Practice question · Multiple choice

Torque is a cross product, and a longer spanner loosens a stubborn bolt more easily. Which feature of the cross product does the spanner exploit?

Hints
  1. Torque is r × F. Which of the two vectors does the spanner's length change?
  2. The magnitude is |r||F|sin θ. Ask which factor you are buying.
Show the answer

D. That its magnitude scales with the distance from the pivot

Why

You are buying |r|. The magnitude |r||F|sin θ scales with the lever arm, so a handle twice as long delivers twice the torque from the same push. The sin θ term earns its place too: pushing along the spanner rather than across it gives zero, which is why you push perpendicular without thinking about it.

Read the lesson: Cross Product and Geometry in Space →

Practise Cross Product and Geometry in Space

The app has 5 more questions on this lesson, and keeps your place in the course. Mathematics I is free to start.

More questions on Cross Product and Geometry in Space