What is the dot product of #<3,4,1 ># and #<5,-1,2 >#?

1 Answer
Bio
Dec 19, 2015

13

Explanation:

  1. Dot product is distributive.
    (e.g. #a*(b+c)=a*b+a*c#)

  2. Dot product of 2 vectors that are perpendicular is zero
    (e.g. #hati\*hatj=0#)

#(3hati+4hatj+hatk) \* (5hati-hatj+2hatk)#

# = (3hati)\*(5hati) + (3hati)\*(-hatj) + (3hati)\*(2hatk)#

#color(white)(s) + (4hatj)\*(5hati) + (4hatj)\*(-hatj) + (4hatj)\*(2hatk)#

#color(white)(s) + (hatk)\*(5hati) + (hatk)\*(-hatj) + (hatk)\*(2hatk)#

# = 15 + 0 + 0 #

#color(white)(s) + 0 - 4 + 0 #

#color(white)(s) + 0 + 0 + 2 #

# = 13 #

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