1.

Given that, `vecr = 2 hat i + 2 hatj` and `vec F = 2 hat i + 6 hat k`. Find the magnitude of torque.

Answer» We know that, `vec tau = vecr xx vec F`
`rArr vec r(2hat i + 3 hat j) xx (2 hat i + 6 hatk)`
=`12(-hatj) + 6 (-hatk) + 18 hat i`
=`-12 hat j - 6 hat k + 18 hat i`
[Note : `hat ixx hat i= 0, hat ixx hat j = k, hat j xx hat i= -K` etc]
Now, `|vectau| = sqrt((-12)^(2) +(-6)^(2) + (18)^(2))`
=`sqrt(144 + 36 +324) = sqrt(504)`.


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