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
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
which is exactly what they said it should be :)