The moment about the point M(-2, 4, -6) of the force represented in magnitude and position AB, where the points A and B have the coordinates (1, 2, -3) and (3, -4, 2) respectively, is

Options

A. `8hati-9hatj-14hatk`
B. `2hati-6hatj+5hatk`
C. `-3hati+2hatj-3hatk`
D. `-5hati-8hatj-8hatk`

Answer

A

Explanation

Force `F= A=(3-1) hati +(-4-2)haj +(2+3)hatk`
`= 2 hati - 6 hatj +5hatk`
Moment of force F with respect to M `=MAxxF `
` :' MA =(1+2)hati +(2-4)hatj+(-3+6)hatk =3hati- 2hatj + 3 hatk`
Now `,MA xxF =|{:(hati,hatj,hatk),(3,-2,3),(2,-6,5):}|`
`=hati (-10+18)-hatj (15-6)+hatk(-18+4)`
`=8 hati -9hatj -1hatk`