Ok i was going through this question on MSE How to prove the distributive property of cross product In A.P.'s answer,Can someone explain me why the sum of areas of triangles formed by a,b and a,c is equal to area of the bigger triangle formed by a,b+c ? Please tell me only if you have a pure geometrical logic,don't use vector theory.Thanks.
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1You don't add the areas of triangles formed by a,b and a,c directly. You have to add them vectorially. – Arpan Apr 05 '15 at 12:00
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But why?Can you explain?..btw dont mind..i'm new to this :-P – Apr 05 '15 at 12:03
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1When you take magnitude of the right-hand side, you get $|a \times b + a \times c|$ and not $|a \times b| + |a \times c|$. – Arpan Apr 05 '15 at 12:07
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I got it...thanks :-) – Apr 05 '15 at 12:10