Friday

August 1, 2014

August 1, 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 :)

**Related Questions**

Calculus - Dot Product - consider a rhombus ABCD a) find the resultant of vector...

Calculus - Two force vectors act on an object and the dot product of the two ...

calculus - Find two unit vectors that make an angle of 60° with v = ‹3, 4›. Give...

linear algebra - show that if u (dot) v = 0 for all vectors v, then u = 0. One ...

Math - Vectors - If "u = (2,2,-1)", "v = (3,-1,0)" and "w = (1,7,8)", verify ...

Physics/Math - A force F = (4.0 N)i + cj acts on a particle as the particle goes...

Mathematics - Dot Product - Consider rhombus ABCD a) Find the resultants of ...

Vectors - When do you use the dot product and the cross product?

Physics (vectors) - Given vectors A= (Axi + Ayj), B= (Byj+Bzk) and C= (Cyj + Czk...

PHYSICS VECTORS - 1. The problem statement, all variables and given/known data ...