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Question
Find the angle between the vectors
`hat"i" - hat"j"` and `hat"j" - hat"k"`
Solution
Let θ be the angle between the given vectors, then
cos θ = `((hat"i" - hat"j") (hat"j" - hat"k"))/(|hat"i" - hat"j"| |hat"j" - hat"k"|)`
= `((hat"i" - hat"j" + 0hat"k")(0hat"i" + hat"j" - hat"k"))/(|hat"i" - hat"j"| |hat"j" - hat"k"|)`
= `((1)(0) + (-1)(1) + (0)(-1))/(sqrt(1^2 + (-1)^2 + 0^2) sqrt(0^2 + (1)^2 + (-1)^2`
= `(0 - 1 + 0)/(sqrt(1 + 1 - 0) sqrt(0 + 1 + 1)`
= `(-1)/(sqrt(2)*sqrt(2)`
cos θ = `-1/2`
cos θ = `- cos(pi/3) = cos(pi - pi/3)`
cos θ = `cos((3pi - pi)/3) = cos (2pi)/3`
θ = `(2pi)/3`
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