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September 16, 2014

September 16, 2014

Posted by **Anonymous** on Thursday, February 21, 2008 at 4:28pm.

"(3a + 4b) product dot (5a + 6b)"

Textbook answer: 15| a |^2 + 38a product dot b + 24| b |^2

- Math - Product Dot Vectors -
**Damon**, Thursday, February 21, 2008 at 5:15pma 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 :)

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