First slide

Vectors

Question

The radius vector of a point is r = (i - 2 j +3 k) m and a force F = (4 i + 5j) acts at that point. The moment of the force in Nm is

Moderate

A

-15i+12j+13k
B

15i-12j+13k
C

-15i-12j+13k
D

15i+12j+13k

Solution

The moment of the force is given by $\vec{τ} = r \times F$
$\begin{array}{l} = (i - 2 j + 3 k) \times (4 i + jj) \\ = |\begin{array}{rrr} i & j & k \\ 1 & - 2 & + 3 \\ 4 & 5 & 0 \end{array}| \\ = i (0 - 15) + j (12 - 0) + k (5 + 8) \\ = - 15 i + 12 j + 13 k \end{array}$

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