How do you compute the dot product to find the magnitude of #u=<2, -4>#?

1 Answer
Steve M
Nov 1, 2016

Inner Product Definition
If # vecu = <<(u_1, u_2, u_3)>> #, and # vecv = <<(v_1, v_2, v_3)>> #, then the inner product (or dot product), a scaler quantity, is given by:
# vecu * vecv = u_1v_1 + u_2v_2 + u_3v_3 #

Inner Product = 0 #hArr# vectors are perpendicular
Also, # |vecu| = sqrt( vecu * vecu ) #

With # vecu = <<2,-4>> => |vecu| = sqrt( (2)(2) + (-4)(-4) ) #
# :. |vecu| = sqrt( 4 + 16 ) #
# :. |vecu| = sqrt( 20 ) #
# :. |vecu| = sqrt( 4xx5 ) #
# :. |vecu| = 2sqrt( 5 ) #

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