(2j×3i).k=? My text book says the answer is -6. But how?

1 Answer
Ananda Dasgupta
Jun 24, 2018

See below

Explanation:

#2 hat j times 3 hat i = 2times 3 (hat j times hat i) = 6(-hat i times hat j) = -6 hat k#

Thus

#(2 hat j times 3 hat i )cdot hat k = -6\ hat k cdot hat k = -6 #

Here we have used the following properties

  • #vec A times vec B = -vec B times vec A#
  • #hat i times hat j = hat k#
  • #hat k cdot hat k = |hat k|^2=1#

You could of course also use the determinant form for the scalar triple product

#(2 hat j times 3 hat i )cdot hat k = hat k cdot (2 hat j times 3 hat i )#
#qquadqquad qquad qquadqquad quad = |(0,0,1),(0,2,0),(3,0,0)|=-6#
but this will be an overkill for this problem.

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