anonymous
  • anonymous
The diagram shows a solid cyclinder standing ona horizontal circular base, centre O and radius 4 units. The line BA is a diameter and the radius OC is at 90 degrees to OA. Points O', A', B' and C' lie on the upper surface of the cyclinder such that OO', AA', BB' and CC' are all verticle and of length 12 untis. The mid-point of BB' is M. Unit vectors i, j, and k are parallel to OA, OC, and OO' respectively. (i) Express each of the vectors MO and MC' in terms of i,j and k.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
|dw:1332672477345:dw|
anonymous
  • anonymous
O is beneath K, J, and i
Callisto
  • Callisto
OB = -4i OM = -4i +6k (since the height is half of BB')

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Callisto
  • Callisto
OC' = 4j +12k ... i hope so... (i'm really bad in vector)
Callisto
  • Callisto
OM + MC' = = OC'
hoblos
  • hoblos
M(-4,0,6) C'(0,4,12) OM= (-4,0,6) = -4i+6k MC' = (4,4,6) = 4i+4j+6k
anonymous
  • anonymous
I thought it was MO?
.Sam.
  • .Sam.
MO=-6k+4i
Callisto
  • Callisto
MO = -OM.. sorry..
.Sam.
  • .Sam.
MC'=4i+4j+6k
anonymous
  • anonymous
Isn't MO, what Sam wrote?
.Sam.
  • .Sam.
|dw:1332673236614:dw|
Callisto
  • Callisto
OM + MC' = OC' (-4i +6k) +MC' = 4j +12k MC' = 4i +4j + 6k
.Sam.
  • .Sam.
MC'=4i+4j+6k
Callisto
  • Callisto
MO = -OM = -(-4i +6k) = 4i-6k
.Sam.
  • .Sam.
|dw:1332673319345:dw| MO=4i-6k
anonymous
  • anonymous
Thanks :) Also, a second part to this question is (ii) Hence find the angle OMC'
Callisto
  • Callisto
angle OMC' = MO . MC' / [|MO||MC'|]
anonymous
  • anonymous
Um, I don't understand that, Callisto
Callisto
  • Callisto
sorry, cos angle OMC' = MO . MC' / [|MO||MC'|]
anonymous
  • anonymous
I still don't understand...
.Sam.
  • .Sam.
MO=-6k+4i MC'=4i+4j+6k \[\cos \theta=\frac{\left[\begin{matrix}4 & \\0 & \\ -6 \end{matrix}\right]\left[\begin{matrix}4 & \\4 & \\ 6 \end{matrix}\right]}{\sqrt{4^{2}+6^{2}}\sqrt{4^{2}+4^{2}+6^{2}}}\]
Callisto
  • Callisto
have you learnt the scalar product of a and b? (a and b are two vectors)
anonymous
  • anonymous
A long time ago. Can you remind me?
.Sam.
  • .Sam.
\[\cos \theta=\frac{16-36}{{2\sqrt{13}*2\sqrt{17}}}\]
Callisto
  • Callisto
|dw:1332673811334:dw|
Callisto
  • Callisto
Hmmm that 0 you see is theta..
Callisto
  • Callisto
|a| is the magnitude of the vector a so similar for b
anonymous
  • anonymous
why cos?
Callisto
  • Callisto
magnitude = \[\sqrt{x^2+y^2+z^2}\] for the vector xi +yj + zk
anonymous
  • anonymous
Thanks for helping :)
Callisto
  • Callisto
just a minute..
anonymous
  • anonymous
Yes, thank you :)
Callisto
  • Callisto
Copyright problem.. I need to delete it :(

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