Shortest Distances - Lines (Edexcel A-Level Further Mathematics): Quizzes

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Shortest Distances - Lines
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What type of distance is calculated between two skew lines in 3D space?

Perpendicular distance

What does b1\mathbf{b}_1 represent in the distance formula between two lines?

Direction vector of line 1

What does a1\mathbf{a}_1 represent in the distance formula between two lines?

A point on line 1

For distance from point p\mathbf{p} to line r=a+λb\mathbf{r} = \mathbf{a} + \lambda \mathbf{b}, what is the denominator?

∣b∣|\mathbf{b}|

In the worked example, what is b1×b2\mathbf{b}_1 \times \mathbf{b}_2?

(1−216)\begin{pmatrix} 1 \\ -2 \\ 16 \end{pmatrix}

In the worked example, what is a2−a1\mathbf{a}_2 - \mathbf{a}_1?

(−2−2−1)\begin{pmatrix} -2 \\ -2 \\ -1 \end{pmatrix}

In the worked example, what is ∣b1×b2∣|\mathbf{b}_1 \times \mathbf{b}_2|?

261\sqrt{261}

In the worked example, what is the dot product (a2−a1)⋅(b1×b2)(\mathbf{a}_2 - \mathbf{a}_1) \cdot (\mathbf{b}_1 \times \mathbf{b}_2)?

−14-14

What is the final distance between the two lines in the worked example?

14261\frac{14}{\sqrt{261}}

What operation is in the numerator of the point-to-line distance formula?

(p−a)×b(\mathbf{p} - \mathbf{a}) \times \mathbf{b}

Which cross product appears in the denominator for distance between two lines?

b1×b2\mathbf{b}_1 \times \mathbf{b}_2

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