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EXAMPLE 3Finding a Cross Product Using Determinants

If v=2ij+k and w=4i+2jk, find

  1. (a) v×w
  2. (b) w×v
  3. (c) v×v

Solution (a) v×w=|ijk211421|=(12)i(24)j+(4+4)k=i+6j+8k

(b) w×v=|ijk421211|=(21)i(4+2)j+(44)k=i6j8k=(v×w)

(c) v×v=|ijk211211|=0i0j+0k=0