The vectors a, b, and c are such that a+b+c=0. Determine the value of (a)(b)+(a)(c)+(b)(c) if |a|=1, |b|=2, and |c|=3.

The Answer should be -7, but can someone show me how to do this please.

Question

The vectors a, b, and c are such that a+b+c=0. Determine the value of (a)(b)+(a)(c)+(b)(c) if |a|=1, |b|=2, and |c|=3.

The Answer should be -7, but can someone show me how to do this please.

rulnick · Answer

a=-1
b=-2
c=3
so
ab=2
ac=-3
bc=-6
and the sum is -7

anonymous · Answer

how did you make a and b negative, I know the magnitude is always positive.

amistre64 · Answer

3 vectors with 0 displacement is a triangle

anonymous · Answer

yes, but that still doesn't explain how a and b vectors are negative.

amistre64 · Answer

negaitve is direction; not magnitude

amistre64 · Answer

i cant verify rulns assessment; but a negative vector is just a direction

amistre64 · Answer

|-3| = 3  for instance

amistre64 · Answer

is (a)(b)  suggest we dot product it?

anonymous · Answer

yea this question is based on the dot product properties.

amistre64 · Answer

and are the vectors in R^2?  or rather, the xy-plane?  or are they general n-tuples?

anonymous · Answer

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