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hey everybody um so were going to take a look at this uh problem about dot products um which essentially is showing us pointing out to us or asking us about a cancellation rule for dot products right what i mean by that is um uh different texts call it different things but we know this from uh well somewhere in your past if i have two numbers like a number a and b and i know that a times b is equal to a times c and a is not zero then it follows that these are the same number right so if i have something like uh 2 times x equals 2 times y then it has to be the case that x equals y right youve used this kind of reasoning before okay this is we might call the cancellation rule so this question is asking is asking the exact same idea if that exact same idea exists for vectors right so if we have a non-zero vector a and we know that the dot products between a and another vector b is the same as the dot products between a and a vector c does it follow that they must be the same vector so