Find the possible values of the constant alpha, given that the vectors a=<alpha,8,3 alpha+1> and b=<alpha+1,alpha-1,-2> are perpendicular to each other

Davirnoilc 2022-11-20 Answered
Find the possible values of the constant α, given that the vectors a =< α , 8 , 3 α + 1 > and b =< α + 1 , α 1 , 2 > are perpendicular to each other
For this question do I have to assume a.b=0?
how can I find the value of constants?
my understanding is: < α , 8 , 3 α + 1 >< α + 1 , α 1 , 2 >= 0
how do I proceed from here to find the values of constant 𝛼?
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Answers (2)

postotnojeyf
Answered 2022-11-21 Author has 16 answers
Given a fixed number z, you can take each q Q and find the unique y q R such that z + y q = q. Since each y q is unique, clearly there are only countably many numbers with that can be found.
So out of the entire pool of | R | things that can go into the y of " z + y", only countably many will yield a rational number, and the rest (uncountably many) will yield an irrational number.
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Brenda Jordan
Answered 2022-11-22 Author has 3 answers
Yes if the vectors are perpendicular, their dot product is 0. Then use a⋅b = i = 1 n a i b i . Then α ( α + 1 ) + 8 ( α 1 ) 2 ( 3 α + 1 ) = 0
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