Turn on thread page Beta
    • Thread Starter
    Offline

    0
    ReputationRep:
    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
    Offline

    0
    ReputationRep:
    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 ?
    • Thread Starter
    Offline

    0
    ReputationRep:
    yeah its me. alright olly! and yeah that makes sense.. good job u corrected me, my teacher said the book was wrong lol!

    hiroki
 
 
 

University open days

  1. University of Cambridge
    Christ's College Undergraduate
    Wed, 26 Sep '18
  2. Norwich University of the Arts
    Undergraduate Open Days Undergraduate
    Fri, 28 Sep '18
  3. Edge Hill University
    Faculty of Health and Social Care Undergraduate
    Sat, 29 Sep '18
Poll
Which accompaniment is best?

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.