## IB Maths HL Vectors, 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

### IB Maths HL Vectors, Dot Product

IB Mathematics HL – Vectors, Dot Product, scalar product

If $a= \begin{pmatrix} 1 \\ 2 \\ 4 \end{pmatrix}$

$b= \begin{pmatrix} 3 \\ -2 \\ 5 \end{pmatrix}$

How can we find the dot product $a \cdot b$ ?

Thanks
elizabeth

Posts: 0
Joined: Mon Jan 28, 2013 8:09 pm

### Re: IB Maths HL Vectors, scalar Product

IB Mathematics HL – Vectors, Dot Product, scalar product, inner product

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

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

another expression of dot product is

$a \cdot b= a_{1} b_{1}+ a_{2} b_{2}+ a_{3} b_{3}$

where

$a= \begin{pmatrix} a_{1} \\ a_{2} \\ a_{3} \end{pmatrix}$

$b= \begin{pmatrix} b_{1} \\ b_{2} \\ b_{3} \end{pmatrix}$

The result of the dot product is a scalar

Thus

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

Hope these help!
miranda

Posts: 268
Joined: Mon Jan 28, 2013 8:03 pm

### IB Mathematics HL Vectors, Dot Product

Thanks miranda!!
elizabeth

Posts: 0
Joined: Mon Jan 28, 2013 8:09 pm