How do you find the inner product and state whether the vectors are perpendicular given #<-2,4,8>*<16,4,2>#?

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Answer 1 · 2016-10-24T11:08:33

# =0 # and perpendicular.

for two vectors

#veca = < a_1,a_2,a_3># and # vecb= < b_1,b_2,b_3>#

the inner (dot) product is calculated by

#color(blue)(veca.vecb=a_1b_1+a_2b_2+a_3b_3)#

so #< -2, 4, 8 >.<16, 4, 2>#

#=-2xx16+4xx4+8xx2#

#=-32+16+16#

#=0#

For two vectors #veca# and #vecb# to be perpendicular

#color(blue)(veca_|_vecb) iff color(blue)(veca.vecb=0)#

the two vectors in the question give inner product 0 #:.# perpendicular.