Question

A force F=(2hati+3hatj+4hatk)N is acting at point P(2m,-3m,6m) find torque of this force about a point O whose position vector is (2hati-5hatj+3hatk) m.

Answer 1

Given:

F = (2hati+3hatj+4hatk)N   is acting at point P(2m,-3m,6m)

Point O whose position vector is (2hati-5hatj+3hatk) m.

To Find:

Torque of this force about a point O

Solution:

We know that , Torque = Force x Perpendicular distance.

In Vector form,

• T = r X F

Here,

• r = PO = 2i -3j + 6k - ( 2i - 5j + 3k) = 2j + 3k m

• F = 2i + 3j + 4k N

• r X F = $\left[\begin{array}{ccc}i&j&k\\0&2&3\\2&3&4\end{array}\right]$
• r X F = i ( 8 - 9 ) - j ( 0 - 6 ) + k ( 0 - 4 )
• T = -i + 6j - 4k Nm