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Solve the following.
Find the Cartesian equation of the line passing through the points and .
Find the Cartesian equation of the line passing through the points $(-1, 0, 2)$ and $(3, 4, 6)$.
Answer
Answer
AIDirection ratios: $(3-(-1), 4-0, 6-2) = (4, 4, 4)$, i.e. $(1, 1, 1)$.
Line through $(-1, 0, 2)$: $\frac{x+1}{1} = \frac{y-0}{1} = \frac{z-2}{1}$.
Hence the Cartesian equation is $x + 1 = y = z - 2$.
Final answer: $\frac{x+1}{1} = \frac{y}{1} = \frac{z-2}{1}$
From ISC 2018 Specimen Mathematics Paper 1, question 15(c).
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