## Vector equation of a line 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

### Vector equation of a line 3D

Vectors, 3D Vector equation - IB Maths HL

How can we find the vector equation of the line passing through the point (-1,2,3) and is parallel to the vector $b= \begin{pmatrix} -1 \\ 5 \\ 7 \end{pmatrix}$ ?

Thanks
lora

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Joined: Wed Apr 10, 2013 7:36 pm

### Re: Vector equation of a line 3D

Vectors, Vector equation of a line - IB Maths HL

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

$r= \begin{pmatrix} -1 \\ 2 \\ 3 \end{pmatrix}+ \lambda \begin{pmatrix} -1 \\ 5 \\ 7 \end{pmatrix}$

Hope these help!
lily

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Joined: Mon Jan 28, 2013 8:04 pm

### Re: Vector equation of a line 3D

Thanks Lily!!
lora

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