Lesson Worksheet: Moment of a Force about a Point in 3D Mathematics

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In this worksheet, we will practice finding the moment of vector forces acting on a body about a point in 3D.

Q1:

True or False: If the force F acts at point 𝐴, then its moment in 3D space about point 𝐵 is given by 𝐵=𝐴𝐵×F.

  • AFalse
  • BTrue

Q2:

If a force Fijk=6−7−8 is acting at a point 𝐴(5,−8,11), find the magnitude of the component of the moment of F about the 𝑦-axis.

  • A106 units of moment
  • B141 units of moment
  • C260 units of moment
  • D13 units of moment

Q3:

The moment of the force F about the origin is 𝑀O, where Fijk=−2− and 𝑀=20+27−34Oijk. Given that the force passes through a point whose 𝑦-coordinate is 4, find the 𝑥 and 𝑧 coordinates of the point.

  • A𝑥=−30, 𝑧=24
  • B𝑥=−19, 𝑧=−8
  • C𝑥=15, 𝑧=12
  • D𝑥=42, 𝑧=28

Q4:

If the force Fijk=𝑚+𝑛− is acting at a point whose position vector is rijk=14−+12 and the 𝑥- and 𝑦-components of the moment of the force F about the origin point are 73 and 242 units of moment, respectively, find the values of 𝑚 and 𝑛.

  • A𝑚=21, 𝑛=6
  • B𝑚=20, 𝑛=−7
  • C𝑚=4, 𝑛=−20
  • D𝑚=19, 𝑛=−6

Q5:

Find the moment M of the force F about the origin point, given that Fijk=−2++, and is acting at a point 𝐴 whose position vector is rijk=6+6−3 with respect to the origin point, then determine the length 𝐿 of the perpendicular segment drawn from the origin point to the line of action of the force F.

  • AMijk=3+12−6, 𝐿=3√302 length units
  • BMik=9+18, 𝐿=3√302 length units
  • CMik=9+18, 𝐿=3√142 length units
  • DMijk=3+12−6, 𝐿=3√142 length units

Q6:

A force Fijk=5+2+3 acts at point 𝐴(−1,4,2). Find the moment of this force about the point 𝐴.

Q7:

In the figure, if the forces Fijk=−7−+3 and Fijk=−7+8−6 are acting on the point 𝐴, where F and F are measured in newtons, determine the moment vector of the resultant about the point 𝑂 in newton-centimeters.

  • A224−102−99ijk
  • B231−85−92ijk
  • C−99−102+224ijk
  • D−92−85+231ijk

Q8:

The forces F=5√673N and F=16√569N act along 𝐴𝐵 and 𝐴𝐶, respectively, as shown in the figure. Given that i, j, and k are a right system of unit vectors in the directions of 𝑥, 𝑦, and 𝑧, respectively, find the sum of the moments of the forces about point 𝑂 in newton-metres.

  • A640+2,640ij
  • B2,773+1,626ij
  • C640+1,626ij
  • D2,773+2,640ij

Q9:

In the figure, determine the sum of the moment vectors of the forces 86 and 65 newtons about 𝑂 in newton-centimeters.

  • A−516+688ik
  • B−867+312+220ijk
  • C−351+312−468ijk
  • D−867+624+220ijk

Q10:

A force of magnitude 6 N is acting on 𝐶 and is represented by a vector in a plane perpendicular to the 𝑦-axis as shown in the figure. Determine its moment vector about 𝐴 in newton-centimeters.

  • A−48√3+72−48ijk
  • B48√3+72−48ijk
  • C72−48√3+48ijk
  • D−48√3−72+48ijk

This lesson includes 23 additional questions and 198 additional question variations for subscribers.

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