MHB What is the Dot Product of u+v?

[karush]

$$u=\left\langle - 2,3\right\rangle v=\left\langle 3,-4 \right\rangle$$
$$\left(u+v\right)\cdot\left(2u+5v\right)=\left\langle 11,14 \right\rangle$$

But the book answer is 25?

 

[topsquark]

$$u=\left\langle - 2,3\right\rangle v=\left\langle 3,-4 \right\rangle$$
$$\left(u+v\right)\cdot\left(2u+5v\right)=\left\langle 11,14 \right\rangle$$

But the book answer is 25?

It looks like you stopped somewhere in the middle, but there's a sign error.

The dot product produces a scalar and you have a vector. Let's take a look.
u + v = <1, -1> and 2u + 5v = <11, -14>. Now dot these together.

-Dan

Addendum: Your thread title is (u + v) x (2u + 5v). There is another vector product called the cross product and is written A x B. Try to avoid the x's. The cross product here gives a vastly different answer.

 

[karush]

Yes, it was dot product

Not sure how to put the dot in the title.

 

[topsquark]

Yes, it was dot product

Not sure how to put the dot in the title.

There are two options I've seen. The first is to write x dot y. The second is to write x.y

-Dan