The Vector Equation of a Line (AQA A-Level Further Maths): Quizzes

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The Vector Equation of a Line
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In the equation r=a+λb\mathbf{r} = \mathbf{a} + \lambda\mathbf{b}, what is λ\lambda?

A scalar parameter

For line r=a+λb\mathbf{r} = \mathbf{a} + \lambda\mathbf{b}, what point is reached when λ=0\lambda = 0?

The point with position vector a\mathbf{a}

How do you find the direction vector for a line through points p\mathbf{p} and q\mathbf{q}?

Subtract one position vector from the other

For Cartesian form x23=y+12=z45\frac{x-2}{3} = \frac{y+1}{-2} = \frac{z-4}{5}, what is the direction vector?

(325)\begin{pmatrix} 3 \\ -2 \\ 5 \end{pmatrix}

If direction vector has zero j-component, where does line lie?

On a plane where y is constant

To check if point lies on line, what must be true?

Same λ\lambda value from all components

What conditions mean two equations represent the same line?

Parallel directions and a common point

What are skew lines?

Not parallel and don't intersect

When solving two line equations gives inconsistent λ\lambda values, the lines are:

Skew

Parametric equations express coordinates as:

Functions of parameter λ\lambda

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