Question

Q. Find the torque of a force 7i+3j-5k about the origin. The force acts as on a partical whose position vector is i-j+k .

Answer 1

The answer is given below :

Force (f) = (7i + 3j - 5k) and
Point (r) = (i - j + k).

So, torque (τ)

= f × r

.....| i j k |
= | 7 3 -5 |
....| 1 -1 1 |

= (3 - 5)i - (7+ 5)j + (-7 -3)k

= (- 2i - 12j - 10k)

and the magnitude of the torque be

$\sqrt{ {( - 2)}^{2} + {( -1 2)}^{2} + {( - 10)}^{2} } \\ \\ = \sqrt{4 + 144 + 100} \\ \\ = \sqrt{248} \\ \\ = 15.44 \: units \: (approximately)$

Thank you for your question.