IB Maths HL Vectors, Dot Product

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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