## IB Maths HL Vectors, Lines 3D

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### 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

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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

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