# Worksheet: Moments in 3D

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

Q1:

The moment of the force about the origin is , where and . Given that the force passes through a point whose -coordinate is 4, find the and coordinates of the point.

• A,
• B,
• C,
• D,

Q2:

If the force is acting at a point whose position vector, with respect to the origin point, is , and the components of the moment of the force about the -axis and the -axis are 73 and 242 units of moment, respectively, find the values of and .

• A,
• B,
• C,
• D,

Q3:

The forces and act along and , respectively, as shown in the figure. Given that , , and are a right system of unit vectors in the directions of , , and , respectively, find the sum of the moments of the forces about point in newton-metres. • A
• B
• C
• D

Q4:

In the figure, a force of magnitude 42 newtons is acting along diagonal in a rectangular prism whose dimensions are 18 cm, 18 cm, and 9 cm. Determine the vector moment of the force about in newton-centimeters. • A
• B
• C
• D

Q5:

If the force , where , is acting on the point , and the moment of the force about the point is , determine the value of .

Q6:

In the figure, determine the sum of the moment vectors of the forces 86 and 65 newtons about in newton-centimeters. • A
• B
• C
• D

Q7:

If a force is acting at a point , find the magnitude of the component of the moment of about the -axis.

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

Q8:

The forces , , and are acting at a point. If the moment vector of the resultant of these forces about the origin point is , find the intersection point of the line of action of the resultant with the -axis.

• A
• B
• C
• D

Q9:

If the force is acting at the point and the two components of the moment of about the -axis and the -axis are 12 and 54 respectively, find the values of and .

• A,
• B,
• C,
• D,

Q10:

and , where and are two forces acting at the points and respectively. The sum of moments about the point of origin equals zero. The sum of the moments about the point also equals zero. Determine the values of and .

• A,
• B,
• C,
• D,

Q11:

If the force is acting at a point whose position vector, with respect to the origin point, is , and the component of the moment of the force about the -axis is 9 moment units, find the length of the perpendicular segment drawn from the origin point to the line of action of .

• A length units
• B19 length units
• C3 length units
• D length units

Q12:

In the figure shown, a force of magnitude newtons acts at a point , determine the moment vector of the force about the origin in N⋅m. • A
• B
• C
• D

Q13:

A force having a magnitude of is acting on point in the direction of and another force having a magnitude of is acting on point in the direction of as shown in the figure. If , , and are a right system of the unit vectors in the direction of , , and , respectively, determine the vector sum of the moments of the forces about point in newton-centimeters. • A N⋅cm
• B N⋅cm
• C N⋅cm
• D N⋅cm

Q14:

Given that a force of magnitude 6 N is acting on as in the figure, determine its moment vector about in newton-centimeters. • A
• B
• C
• D

Q15:

In the figure, is a rod fixed to a vertical wall at end . The other end is connected to a wire , where is fixed to a different point on the same vertical wall. If the tension in the wire equals 65 N, calculate the moment of the tension about point in newton-metres. • A
• B
• C
• D

Q16:

If the force is acting at the point , find the moment of the force about the point and then calculate the length of the perpendicular segment from to the line of action of the force.

• A,
• B,
• C,
• D,

Q17:

If a force is acting at the point , where the moment of about the origin is , find .

• A
• B
• C
• D

Q18:

In the figure, if the forces and are acting on the point , where and are measured in newtons, determine the moment vector of the resultant about the point in newton - centimeters. • A
• B
• C
• D

Q19:

Find the moment of the force about the origin point, given that , and is acting at a point whose position vector is with respect to the origin point, then determine the length of the perpendicular segment drawn from the origin point to the line of action of the force .

• A, length units
• B, length units
• C, length units
• D, length units

Q20:

If acts at a point , and the moment of about the origin point is equal to , find the value of .