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EXAMPLE 2Adding and Subtracting Vectors Algebraically

If v=2,3,1 and w=1,2,4, find:

  1. (a) v+w
  2. (b) wv
  3. (c) 12w
  4. (d) 2v+3w

Solution

(a) v+w=2,3,1+1,2,4=2+(1),3+(2),1+4=1,1,3

(b) wv=1,2,42,3,1=12,23,4(1)=3,5,5

(c) 12w=121,2,4=12(1),12(2),12(4)=12,1,2

(d) 2v+3w=22,3,1+31,2,4=4,6,2+3,6,12=1,0,10