Question

The textbook answer is -80
Question: find (3a+4b)(2b+4a)
if a= -i-3j+k and b=2i+4j-5k

What I did:
=6(a)(b) - 12|a|^2 + 2|b|^2 - 4(a)(b)
=2(a)(b)-12|a|^2+2|b|^2
substitute a and b with given equations.
Added like terms for each part.(too long to write out)
and I got -20-6+38+4-24^2-4^2-10^2+2-18+1+8+32+50 (I made all a's and b's the value of 1)
=-601
Whaaaaat?

Answer 1

I will use the notation:
a = -i-3j+k = <-1,-3,1>
b = 2i+4j-5k = <2,4,-5>

and (3a+4b)(2b+4a) is the dot product

= ( <-3,-9,3> + <8,16,-20>) dot (<4,8,-10> + <-4,-12,4>)
= <5,7,-17> dot <0,-4,-6>
= 0 -28 + 102
= 74

check my arithmetic, since I did not get -80