Pure · Vectors
Chapter 1 · 3
The idea
The vector equation of a line
Describing a line in space as r = a + tb — a point on it plus a direction — and using it to test whether a point lies on a line, to decide whether two lines are parallel, intersecting or skew, to find the point of intersection, and to find the acute angle between two lines.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
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Pure · Vectors
The vector equation of a line
Describing a line in space as r = a + tb — a point on it plus a direction — and using it to test whether a point lies on a line, to decide whether two lines are parallel, intersecting or skew, to find the point of intersection, and to find the acute angle between two lines.
Why it works
A point and a direction
To pin down a line you need just two things: one point it passes through and which way it goes. If is the position vector of a known point on the line and is any vector along it (a direction vector), then every point on the line is reached by starting at and walking some multiple of : The parameter is a dial: each value of gives one point, and sweeping through all real numbers sweeps out the whole line. Negative simply walks backwards.Keep reading — free
The rest of the explanation, plus 3 worked examples you step through move by move.
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