The vertices of a quadrilateral are A(1,2,-1),B(-4,2,-2),C(4,1,-5)and D(2,-1,3).Forces of magnitudes 2,3,2 N are acting at point A along the lines AB,AC,AD respectively. Find their resultant[a](10i - 9j + 6k)/√26[b](i - 9j - 6k)/√26[c](i + 9j + 16k)/√26[d](i - 19j + 6k)/√26

Firstly find ABcap ACcap and ADcap

AB=-5i-1k ABcap=AB/√26

AC=3i-1j-4k ACcap=AC/√26

AD=i-3j+4k ADcap=AD/√26

Now Force(total)=2*ABcap+3*ACcap+2*ADcap

                       =[(-10+9+2)i+(0-3-6)j+(-2-12+8)k]/√26

                       =Option [b]

If you have any doubts regarding the answer feel free  to contact

Do not forget to approve this answer