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Question
Find the angle between the planes `vec"r"*(hat"i" + hat"j" - 2hat"k")` = 3 and 2x – 2y + z = 2
Solution
`vec"n"_1 = hat"i" + hat"j" - 2hat"k"`
`vec"n"_2 = 2hat"i" - 2hat"j" + hat"k"`
`|vec"n"_1| = sqrt(1 + 1 + 4) = sqrt(6)`
`|vec"n"_2| = `sqrt(4 + 4 + 1) = sqrt(9)` = 3
cos θ = `(|vec"n"_1 * vec"n"_2|)/(|vec"n"_1||vec"n"_2|)`
= `(|-2|)/(sqrt(6) xx 3)`
= `2/(sqrt(6) xx 3)`
θ = `cos^-1(2/(3sqrt(6)))`
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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
