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Question
Find the acute angle between the following lines.
`vec"r" = (4hat"i" - hat"j") + "t"(hat"i" + 2hat"j" - 2hat"k")`
Solution
`vec"r" = (hat"i" - 2hat"j" + 4hat"k") + "s"(- hat"i" - 2hat"j" + 2hat"k")`
`vec"b" = hat"i" + 2hat"j" - 2hat"k"`
`vec"d" = -hat"i" - 2hat"j" + 2hat"k"`
`vec"b"*vec"d" = 1(-1) + 2(- 2) - 2(2)`
= – 1 – 4 – 4
= – 9
`|vec"b"* vec"d"|` = 9
`|vec"b"| = sqrt(1 + 4 + 4)`
= `sqrt(9)`
= 3
`|vec"d"| = sqrt(1 + 4 + 4)`
= `sqrt(9)`
= 3
cos θ = `|vec"b" * vec"d"|/(|vec"b"||vec"d"|)`
= `9/(3 xx 3)`
= 1
cos θ = 1
θ = 0°
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