## IB Maths HL Vectors operations

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 operations

IB Mathematics HL – Vectors operations

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

$b= \begin{pmatrix} -1 \\ 4 \\ 5 \end{pmatrix}$

How can we find the vectors $a-2b$ and $3a+2b$

Thanks
elizabeth

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

### Re: IB Maths HL Vectors operations

IB Mathematics HL – Vectors operations, addition, subtraction, scalar multiplication

First of all let me remind you the properties of vector addition

The vector addition (subtraction) is Commutative, Associative, there is an additive identity which is the zero vector ad there is an additive inverse which is the vector with equal magnitude and opposite direction. Also there is the scalar multiplication which is when a vector is multiplied by a scalar.

$a-2b=\begin{pmatrix} 1 \\ 2 \\ 4 \end{pmatrix}-2 \begin{pmatrix} -1 \\ 4 \\ 5 \end{pmatrix}$

$=\begin{pmatrix} 1 \\ 2 \\ 4 \end{pmatrix}-\begin{pmatrix} -2 \\ 8 \\ 10 \end{pmatrix}$

$=\begin{pmatrix} 1+2 \\ 2-8 \\ 4-10 \end{pmatrix}$

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

and

$3a+2b=3 \begin{pmatrix} 1 \\ 2 \\ 4 \end{pmatrix} + 2 \cdot \begin{pmatrix} -1 \\ 4 \\ 5 \end{pmatrix}$

$=\begin{pmatrix} 3 \\ 6 \\ 12 \end{pmatrix} +\begin{pmatrix} -2 \\ 8 \\ 10 \end{pmatrix}$

$=\begin{pmatrix} 1-2 \\ 6-8 \\12-10 \end{pmatrix}$

$=\begin{pmatrix} -1 \\ -2 \\ 2 \end{pmatrix}$

Hope these help!
lily

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

### Re: IB Maths HL Vectors operations

lily wrote:IB Mathematics HL – Vectors operations, addition, subtraction, scalar multiplication

First of all let me remind you the properties of vector addition

The vector addition (subtraction) is Commutative, Associative, there is an additive identity which is the zero vector ad there is an additive inverse which is the vector with equal magnitude and opposite direction. Also there is the scalar multiplication which is when a vector is multiplied by a scalar.

$a-2b=\begin{pmatrix} 1 \\ 2 \\ 4 \end{pmatrix}-2 \begin{pmatrix} -1 \\ 4 \\ 5 \end{pmatrix}$

$=\begin{pmatrix} 1 \\ 2 \\ 4 \end{pmatrix}-\begin{pmatrix} -2 \\ 8 \\ 10 \end{pmatrix}$

$=\begin{pmatrix} 1+2 \\ 2-8 \\ 4-10 \end{pmatrix}$

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

and

$3a+2b=3 \begin{pmatrix} 1 \\ 2 \\ 4 \end{pmatrix} + 2 \cdot \begin{pmatrix} -1 \\ 4 \\ 5 \end{pmatrix}$

$=\begin{pmatrix} 3 \\ 6 \\ 12 \end{pmatrix} +\begin{pmatrix} -2 \\ 8 \\ 10 \end{pmatrix}$

$=\begin{pmatrix} 1-2 \\ 6-8 \\12-10 \end{pmatrix}$

$=\begin{pmatrix} -1 \\ -2 \\ 2 \end{pmatrix}$

Hope these help!

Thanks miranda!!
elizabeth

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