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Angello90
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Homework Statement
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
Homework Equations
a.b=|a||b|Cosθ
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