How do you compute the dot product for <5, 12>*<-3, 2><5,12>⋅<−3,2>?

1 Answer
Douglas K.
Nov 9, 2016

Please see the explanation of how to compute the dot-product for any two vectors of the same dimension and the answer to the given vectors: < 5, 12 > * < -3, 2 > = 9<5,12>⋅<−3,2>=9

Explanation:

For two dimensional vectors < a_x, a_y > and < b_x, b_y ><ax,ay>and<bx,by>, the dot-product is:

< a_x, a_y > * < b_x, b_y > = (a_x)(b_x) + (a_y)(b_y)<ax,ay>⋅<bx,by>=(ax)(bx)+(ay)(by)

The dot-product is extendable to 3 dimensions and beyond:

For 3 dimensional vectors < a_x, a_y, a_z > and < b_x, b_y, b_z ><ax,ay,az>and<bx,by,bz>, the dot-product is:

< a_x, a_y, a_z > * < b_x, b_y, b_z > = (a_x)(b_x) + (a_y)(b_y) + (a_z)(b_z)<ax,ay,az>⋅<bx,by,bz>=(ax)(bx)+(ay)(by)+(az)(bz)

For n dimensional vectors < a_1, a_2,..., a_n > and < b_1, b_2,..., b_n >, the dot-product is:

< a_1, a_1,..., a_n > * < b_1, b_2,..., b_n > = (a_1)(b_1) + (a_2)(b_2) +..., + (a_n)(b_n)

The dot product for the given vectors is:

< 5, 12 > * < -3, 2 > = (5)(-3) + (12)(2)

< 5, 12 > * < -3, 2 > = -15 + 24

< 5, 12 > * < -3, 2 > = 9

Related questions
See all questions in The Dot Product
Impact of this question
2267 views around the world
You can reuse this answer
Creative Commons License