(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Derive an expression for the scalar product of a and b if the two vectors are written in terms of the usual Cartesian orthogonal triad i, j, k.

By an appropriate choice of a and b, verify the trigonometric identity

cos(θ +ϕ) = cosθ cosϕ − sinθsinϕ

2. Relevant equations

a.b=|a||b|Cosθ

3. The attempt at a solution

So dot product in Cartesian is:

a=(x1)i + (x2)j + (x3)k

b=(y1)i + (y2)j + (y3)k

(x1)(y1) + (x2)(y2) + (x3)(y3) = ((x1)^2+(x2)^2+(x3)^2)^(1/2)((y1)^2+(y2)^2+(y3)^2)^(1/2)Cosθ

But how can I use this to prove the identity mentioned above?

Please send me some ideas.

Cheers

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# Homework Help: Cos(A+B) proof

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