Let θ be the angle between a and b. We know that cosθ = (a∙b) / (|a||b|). Since a and b are unit vectors, |a|=|b|=1. Therefore we need to find a∙b.
a+2b and 5a-4b are perpendicular, so
(a+2b)∙(5a-4b)=0
Multiply this out to obtain
5a∙a + 6a∙b - 8b∙b = 0
which results in
6a∙b = 8b∙b - 5a∙a
Since a and b are unit vectors,
6a∙b = 8-5 = 3
Therefore, cos θ = 3/6. θ=π/3
if vectors a+2b and 5a-4b are perpendicular to each other and a and b are unit vectors. Find the angle between a and b.
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If two vectors are perpendicular their dot product will equal zero.
(a+2b)•(5a-4b)=0
5a•a+10a•b-4a•b-8b•b=0
6a•b=8b•b-5a•a
6a•b=8-5=3
cosθ=3/6.
θ=π/3
(a+2b)•(5a-4b)=0
5a•a+10a•b-4a•b-8b•b=0
6a•b=8b•b-5a•a
6a•b=8-5=3
cosθ=3/6.
θ=π/3