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Grade 11General Physics

THREE FORCES ​​​​ F1=a(i-j+k) F2=2i-3j+4k and F3=8i-7j+6k act simultaneously on a particle.lf the particle is in equilibrium then the value of a is

Profile image of v venu madhavi
7 Years agoGrade 11
Answers icon

1 Answer

Profile image of Arun
7 Years ago
To be in equilibrium, the three forces must add to cancel each other out: 

(2,-3,4)+(8,-7,6)+a(1,-1,1)=(0,0,0) 

we can equate the ith jth and kth component of each side of the equation, 
So ith jth and kth component of each vector must sum to 0: 

2i+8i+ai=0 
-3j-7j-aj=0 
4k+6k+ak=0 

so lets solve one of these equations to find m, say the first one. 

2i+8i+ai=0 

i is not equal to zero, so we can re-write it like this: 

2+8+a=0 
so 
a=-10 

now lets check this by subing it into the other equations: 

-3j-7j+10j=0 

-3-7+10=0 

yep that checks out 

the last one: 

4k+6k-10k=0 

4+6-10=0 

yep that checks out too, 

so a=-10

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