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inner products

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Determine which of the following are inner products in R^3....
x=(x_1, x_2, x_3), y=(y_1, y_2, y_3)

a) <x,y>= x_1 y_1+x_3 y_3
b) <x,y>= x_1 y_1- x_2 y_2 + x_3 y_3
c) <x,y>= 2x_1 y_1 + x_2 y_2 + 4x_3 y_3
d) <x,y>= x^2_1 y^2_1 + x^2_2 y^2_2 + x^2_3 y^2_3

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This solution evaluates inner products.

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Answer: C

Let me explain why a, b, d are not inner product.
a) Let x = ...

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