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# angles between a vector and a plane watch

1. i have the following question...

relative to the origin O, A, B, C and D have position vectors

i + j, i + 1/2j + k, j + k and i + j + k,

respectively

a) calculate the angle between j and the plane ABC

i have got the following solution:

AB = (0 , -1/2, 1)

AC = (0, 1, 1)

AB x AC = (-1/2, -1, -1/2)

j = (0, 1, 0)

(a x b = |a| |b| sin x)

so j x (AB x AC) = (-1/2, 0, 1/2)

so (-1/2, 0, 1/2) = 1 * root(3/2) * sinx

root(2)/2 = root(3/2) * sinx

sinx = root(1/3)

however the answers say sinx = root(2/3)?! where have i gone wrong?... im not sure if it is me or the book.. this book has got quite a few errors!!

hiroki
2. you have done it nearly right. The mistake you have made is that you have worked out the angle between j and the normal vector of the plane, when it wanted the angle between j and the plane itself (so all you have to do is add Pi/2 to your angle).

sinx = root(1/3)
x = 0.615. . .
x + Pi/2 = 2.186. . .
sinx = 0.816 = SQRT[2/3]

ps: are you the same hikori as on OcUK ?
3. yeah its me. alright olly! and yeah that makes sense.. good job u corrected me, my teacher said the book was wrong lol!

hiroki

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