Torque: What is the torque about the origin on a particle located at = 3 m + 4 m - 2 m if a force = 5N - 2 N + 3 N on the particle?
A) (8 + - 26 ) N ∙ m
B) (8 - 19 - 26 ) N ∙ m
C) (8 + 2 + ) N ∙ m
D) (16 - 19 - 26 ) N ∙ m
E) (8 - 2 + ) N ∙ m

Question

Torque: What is the torque about the origin on a particle located at  = 3 m  + 4 m  - 2 m  if a force  = 5N  - 2 N  + 3 N  on the particle?
A) (8 + - 26 ) N ∙ m 
B) (8 - 19 - 26 ) N ∙ m 
C) (8 + 2 + ) N ∙ m 
D) (16 - 19 - 26 ) N ∙ m 
E) (8 - 2 + ) N ∙ m

Quizplus · Accepted Answer

The torque about the origin on a particle is given by the cross product of the position vector and the force, i.e. τ = r x F.

Here, r = 3i + 4j - 2k 
F = 5i - 2j + 3k

Taking the cross product: 
r x F = \begin{vmatrix} i & j & k \ 3 & 4 & -2 \ 5 & -2 & 3 \end{vmatrix}

Expanding this determinant, we get: 
r x F = (8i - 19j - 26k) N ∙ m

Therefore, the correct answer is B.

Torque: What Is the Torque About the Origin on a Particle