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I'm reading the book The Theoretical Minimum. I wonder if two one of the problems in the book can be thought of graphically. The mathematical solution didn't even occur to me, although it make perfect sense and probably should have been obvious.

I know now that if it is orthogonal than θ=∏/2 and cos∏/2=0

Thank you for your time and consideration

**1. Can you explain why the dot product of two vectors that are orthogonal is 0?****2. A dot B= abs(a)abs(b)cosθ**I know now that if it is orthogonal than θ=∏/2 and cos∏/2=0

**Is there a way of visualizing i, j and k to get the same answer?****3. For a second I thought that connecting x, y z together end to end would create a situation that would eliminate distance so the magnitude would equal zero, but after thinking about it a little more before posting this I don't believe that would work. I actually feel like there is something to this line of think though, which is why I'm asking this question.**Thank you for your time and consideration

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