## Scalar Dot Product

Discussions for the Core part of the syllabus. Algebra, Functions and equations, Circular functions and trigonometry, Vectors, Statistics and probability, Calculus. IB Maths HL Revision Notes

### Scalar Dot Product

Vectors, Dot Product, scalar product - IB Maths HL

If $v= \begin{pmatrix} 3 \\ 1 \\ -1 \end{pmatrix}$

$w= \begin{pmatrix} 6 \\ -3 \\ 1 \end{pmatrix}$

How can we find the dot product $v \cdot w$ ?

Thanks
lora

Posts: 0
Joined: Wed Apr 10, 2013 7:36 pm

### Re: Scalar Dot Product

Vectors, Dot Product, scalar product, inner product - IB Maths HL

The dot (scalar) product of two vectors is defined as following

$v \cdot w=|v||w|cos \theta$ , where $\theta$ is the angle between the two vectors.

another expression of scalar product is

$v \cdot w=v_{1} w_{1}+ v_{2} w_{2}+ v_{3} w_{3}$

where

$v= \begin{pmatrix} v_{1} \\ v_{2} \\ v_{3} \end{pmatrix}$

$w= \begin{pmatrix} w_{1} \\ w_{2} \\ w_{3} \end{pmatrix}$

The result of the sclar (inner) product is a scalar (a number)

Thus

$a \cdot b=(1 \cdot 3) + (2 \cdot (-2)) + (4 \cdot 5) =19$

Hope these help!!
lily

Posts: 0
Joined: Mon Jan 28, 2013 8:04 pm

### Re: Scalar Dot Product

Thanks Lily!!
lora

Posts: 0
Joined: Wed Apr 10, 2013 7:36 pm