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Vector area of a triangle

  • Point A has position vector 8i+13j-2k
  • Point B has position vector 10i+14j-4k
  • Point C has position vector 9i+9j+6k
  • The line l passes through the points A and B
  • The point X lies on l, where CX is the shortest distance between C and l
  • Find the area of the triangle CXB, giving your answer to 3 significant figures. (Bonus points for an exact answer.)