Note: Vectors are represented by corresponding capital letters.

The cross product on the right is disassembled by the law of multiplicative distribution: ab-a c-b c+c 2 = 0-(a+b) c+1=1-(a+b) c.

Because a b = 0, and a, b and c are unit vectors. As can be seen from the image, a+b = root number 2, and the maximum value of ∴ (a+b) c is root number 2* 1= root number 2. So the minimum value of the original formula is 1- root number 2.

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