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A slab is subjected to two forces vec F(...

A slab is subjected to two forces `vec F_(1) and vec F_(2)` of same magnitude F as shown in the figure . Force `vec F_(2)` is in XY-plane while force `F_(1)` acts along z-axis at the point `(2 vec I + 3 vec j)` .The moment of these forces about point O will be :

A

`(3hati+2hatj+3hatk)F`

B

`(3hati+2hatj-3hatk)F`

C

`(3hati-2hatj-3hatk)F`

D

`(3hati-2hatj+3hatk)F`

Text Solution

Verified by Experts

The correct Answer is:
D
`tau_(0)=vecr_(1)xxvecF_(1)+vecr_(2)xxvecF_(2)`
`=(2hati+3hatj)xxF(hatk)+6hatjxx((F)/(2)(-hati)+(Fsqrt(3))/(2)(-hatj))`
`=2F(-hatj)+3F(hati)+3F(hatk)+0`
`=(3hati-2hatj+3hatk)F`
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