Vectors question very shoooort

[Questions999]

Vectors question very shoooort :D

we have the vectors a ,b and c with the modules a=2,b=5 and c=7. If a+b+c=0 find a*b+b*c+a*c
Now,i tried a+b=-c and replace but i get nothing in the end..any ideas?

 

[I like Serena]

we have the vectors a ,b and c with the modules a=2,b=5 and c=7. If a+b+c=0 find a*b+b*c+a*c
Now,i tried a+b=-c and replace but i get nothing in the end..any ideas?

Hi Elaia!

Perhaps you could try to evaluate (a+b+c)*(a+b+c) and deduce what you can?

 

[aralbrec]

we have the vectors a ,b and c with the modules a=2,b=5 and c=7. If a+b+c=0 find a*b+b*c+a*c
Now,i tried a+b=-c and replace but i get nothing in the end..any ideas?

It's always a good idea to sketch on paper if you don't know where to start. The first equation gives some key information about the geometrical relationship between a,b,c.

a + b + c = 0

The second equation involves information about the angles between vectors, which would be easy to determine from the sketch above.

a.b + b.c + a.c = 0


But ILikeSerena's solution will get you there the quickest because we aren't talking about one or maybe two angles, but all possible angles between the vectors. That's when you might be inspired to dot the sum of all vectors with itself, which leads to a length squared that you know.