Question

Show that (a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a) = 0

Answer 1

Answer:

a+b+c = 0

a+b = -c

cross product by a on both sides

a×a+b×a=-c×a

b×a = a×c         by vector property

now

a+c = -b  ........(b)

cross product by a on both sides

a×b+b×b=-c×b

a×b=b×c .........(a)         by vector property

henceby comparing equations (a) and (b)

a×b=b×c=c×a

Step-by-step explanation:

Answer 2

Answer:

(a – b) (a + b) + (b – c) (b + c) + (c – a) (c + a) = 0

(a^2 - b^2) + (b^2 - c^2) + (c^2 - a^2) = 0

a^2 - b^2 + b^2 - c^2 + c^2 - a^2 =0

0=0

HENCE PROVED.

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