## IB Maths HL Vectors, Lines 3D

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, Lines 3D

IB Mathematics HL – Vectors, Vector equation of a line 3D

How can we find the vector equation of the line passing through the point (1,4,5) and is parallel to the vector $b= \begin{pmatrix} -2 \\ 1 \\ 4 \end{pmatrix}$ ?

Thanks
elizabeth

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

### Re: IB Maths HL Vectors, Lines 3D

IB Mathematics HL – Vectors, Vector equation of a line 3D

The vector equation of a line is given by the following formula

$r=a+ \lambda b$

where a is a position vector of the line (i.e. a point on the line) , b is a direction vector (i.e. a vector parallel to the line) and $\lambda$ is a real number parameter.
So the vector equation of the line is given by the formula

$r= \begin{pmatrix} 1 \\ 4 \\ 5 \end{pmatrix}+ \lambda \begin{pmatrix} -2 \\ 1 \\ 4 \end{pmatrix}$

Hope these help!
miranda

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

### IB Mathematics HL Vectors, Lines 3D

Thanks miranda!!
elizabeth

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