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

1 Answer
Dec 19, 2015

13

Explanation:

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

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

(3hati+4hatj+hatk) * (5hati-hatj+2hatk)(3ˆi+4ˆj+ˆk)(5ˆiˆj+2ˆk)

= (3hati)*(5hati) + (3hati)*(-hatj) + (3hati)*(2hatk)=(3ˆi)(5ˆi)+(3ˆi)(ˆj)+(3ˆi)(2ˆk)

color(white)(s) + (4hatj)*(5hati) + (4hatj)*(-hatj) + (4hatj)*(2hatk)s+(4ˆj)(5ˆi)+(4ˆj)(ˆj)+(4ˆj)(2ˆk)

color(white)(s) + (hatk)*(5hati) + (hatk)*(-hatj) + (hatk)*(2hatk)s+(ˆk)(5ˆi)+(ˆk)(ˆj)+(ˆk)(2ˆk)

= 15 + 0 + 0 =15+0+0

color(white)(s) + 0 - 4 + 0 s+04+0

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

= 13 =13