What is the dot product of #<5,1,-7># and #<8,4,9>#?

2 Answers

The dot product of two three dimensional vectors is defined as

#a*b=a_x*b_x+a_y*b_y+a_z*b_z#

In our case #a=(5,1,-7)# and #b=(8,4,9)#

hence

#a*b=5*8+1*4-7*9=-19#

Jan 3, 2016

Answer:

#-19#

Explanation:

To do the dot product, you multiply together the corresponding components, and then sum the results. In general:
#(a_1, a_2, a_3)*(b_1, b_2, b_3)=(a_1b_1+a_2b_2+a_3b_3) #

So in your case:

#(5*8)+(1*4)+(-7*9)#
#=40+4-63#
#=-19#