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Question
Find the angle between the vectors `2hat"i" - hat"j" + hat"k"` and `3hat"i" + 4hat"j" - hat"k"`.
Solution
Let `2hat"i" - hat"j" + hat"k"` and `3hat"i" + 4hat"j" - hat"k"`
And let θ be the angle between `vec"a"` and `vec"b"`.
∴ cos θ = `(vec"a" * vec"b")/(|vec"a"||vec"b"|)`
= `((2hat"i" - hat"j" + hat"k")*(3hat"i" + 4hat"j" - hat"k"))/(sqrt(4 + 1 + 1) * sqrt(9 + 16 - 1))`
= `(6 - 4 - 1)/(sqrt(6) * sqrt(26))`
⇒ `1/(2sqrt(3) * sqrt(13)) = 1/(2sqrt(39))`
∴ θ = `cos^-1 1/(2sqrt(39))`
⇒ θ = `cos^-1 (1/156)`
Hence, the required value of θ is `cos^-1 (1/156)`.
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