Math  Product Dot Vectors
posted by Anonymous .
How would you expand and simplify the following equation?
"(3a + 4b) product dot (5a + 6b)"
Textbook answer: 15 a ^2 + 38a product dot b + 24 b ^2

a is evidently a vector and so is b
in that case I would write a and b as
a = Ax i + Ay j
and
b = Bx i + By j
Then 3 a + 4 b = (3Ax+4Bx)i+(3Ay+4By)j
and 5 a + 6 b = (5Ax+6Bx)i+(5Ay+6By)j
Then the dot product of those two vectors is
(3Ax+4Bx)(5Ax+6Bx)+(3Ay+4By)(5Ay+6By)
which is
(15Ax^2+38AxBx+24Bx^2)+(15Ay^2+38AyBy+24By^2)
which is
15(Ax^2+Ay^2)+38(AxBx+AyBy)+24(Bx^2+By^2)
which is exactly what they said it should be :)
Respond to this Question
Similar Questions

linear algebra
show that if u (dot) v = 0 for all vectors v, then u = 0. One of the Axioms an inner product has to satisfy is: x dot x >=0 where equality only holds if x = 0 So, in your problem you take the special case v = u. Then: u dot u = … 
Math  Vectors
If "u = (2,2,1)", "v = (3,1,0)" and "w = (1,7,8)", verify that "u (dot) (v + w) = u (dot) v + u (dot) w". My work: LHS: u (dot) (v + w) = (2,2,1) (dot) (4,6,8) = [(2,2,1) (dot) (3,1,0)] + [(2,2,1) (dot) (1,7,8)] = [u (dot) v] … 
Math: Cross Product
Prove that  a x b  = (sqrt) [(a (dot) b)(b (dot) b)  (a (dot) b)^2] 
Calculus  Dot Product
consider a rhombus ABCD a) find the resultant of vector AB + vector AD and vector AB  vector AD? 
Mathematics  Dot Product
Consider rhombus ABCD a) Find the resultants of vector AB + vector AD and vector AB  vector AD b) What will the value of (vector AB + vector AD) dot product (vector AB  vector AD) always be? 
calculus
Find two unit vectors that make an angle of 60° with v = ‹3, 4›. Give your answers correct to three decimal places. I'm not sure what to do here; I believe that I use to definition of a dot product (or maybe cross product) with … 
Calculus
Two force vectors act on an object and the dot product of the two vectors is 20. If both of the force vectors are doubled in magnitude, what is their new dot product? 
dot product of vecotrs
Question: Find (3a+b)dot(2b4a) if a=i3j+k and b=2i+4j5k I did: =3(1,3,1)+(2,4,5)dot 2(2,4,5)4(1,3,1) =(3,9,3)+(2,4,5)dot(4,8,10)(4+12,4) =(1,5,2)dot(0,4,6) =(0,20,12) =0+20+12 =32 The text book answer is 80. … 
Vectors: Dot product
Given a and b unit vectors if a+b=square root 3, determine (2a5b)dot(b+3a) First I foiled the whole thing: =2(a dot b)+ 6 (a dot a)  5(b dpt b) 15(a dot b) =13(a dot b) + 6(a dot a)  5(b dot b) =13(1)(1)+65 =13+1 =12 Textbook … 
Vectprs and Scalars
Why are some of these scalars and others are vectors?