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TwentyEight

M4TH5 SU<KS

Sep 18th, 2013
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  1. (i) if OA is perpendicular to OC then: OA∙OC = 0
  2. OA∙OC = 1*0 + 2p*q + q*(-2p)
  3. = 2pq - 2pq
  4. = 0
  5. ∴OA is perpendicular to OC
  6.  
  7. (ii) CA = OA - OC
  8. = (i + 2pj + qk) - [-(4p²+q²)i + 2pj + qk]
  9. = (4p²+q²-1)i
  10. |CA| = √(4p²+q²-1)²
  11. = 4p²+q²-1
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