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Question
Find the angle between the vectors
`2hat"i" + 3hat"j" - 6hat"k"` and `6hat"i" - 3hat"j" + 2hat"k"`
Solution
Let θ be the angle between the given vectors, then
cos θ = `((2hat"i" + 3hat"j" - 6hat"k") * (6hat"i" - 3hat"j" + 2hat"k"))/(|2hat"i" + 3hat"j" - 6hat"k"| |6hat"i" - 3hat"j" + 2hat"k"|)`
= `((2)(6) + (3)(- 3) + (- 6)(2))/(sqrt(2^2 + 3^2 + (- 6)^2) sqrt(6^2 + (- 3)^2 + 2^2)`
= `(12 - 9 - 12)/(sqrt(4 + 9 + 36) sqrt(36 + 9 + 4)``
= `(- 9)/(sqrt(49) * sqrt(49)`
= `( - 9)/49`
θ = `cos^-1 ((-9)/49)`
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