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Dont really understand this dot product vector problem ?
(a) 0 (b) -2 (c) 2 (d) 4
Questions about deriving cosine law from dot product (vectors)
There's a triangle made of vectors s a, b and c. c connects the tip of b at its tail to the tip of a at its tip. It can be expressed as;
step 1: b + c = a
step 2: c = a - b
step 3: c^2 = ||a - b||^2
step 4: c^2 = (a - b) ⋅ (a - b)
step 5: c^2 = a^2 + b^2 - 2a ⋅ b
step 6: c^2 = a^2 + b^2 - 2abcosC
Is this accurate? And more specifically, is step 3 accurate? Are you supposed to square both sides? And if you are, why does squaring it turn it into a dot product instead of, say, the cross product?
Secondly, when writing out the steps, do I have to put an arrow above the letters to represent a vector?