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Question
Find the angle between the line `vec"r" = (2hat"i" - hat"j" + hat"k") + "t"(hat"i" + 2hat"j" - 2hat"k")` and the plane `vec"r"*(6hat"i" + 3hat"j" + 2hat"k")` = 8
Solution
`vec"b" = hat"i" + 2hat"j" - 2hat"k"`
`vec"n" = 6hat"i" + 3hat"j" + 2hat"k"`
`vec"b"*vec"n"` = 6 + 6 – 4 = 8
`|vec"b"| = sqrt(1 + 4 + 4) = sqrt(9)` = 3
`|vec"n"| = sqrt(36 + 9 + 4) = sqrt(49)` = 7
sin θ = `(|vec"b"*vec"n"|)/(|vec"b"||vec"n"|)`
= `8/(3 xx 7)`
= `8/21`
θ = `sin^-1(8/21)`
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Choose the correct alternative:
If `vec"a" = hat"i" + hat"j" + hat"k", vec"b" = hat"i" + hat"j", vec"c" = hat"i"` and `(vec"a" xx vec"b")vec"c" - lambdavec"a" + muvec"b"` then the value of λ + µ is
