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The point of intersection of the lines and is:

Mathematics20271 markMCQ
The point of intersection of the lines $\frac{x-1}{2} = \frac{y-2}{3} = \frac{3-z}{-4}$ and $\frac{x-1}{5} = \frac{2-y}{-2} = \frac{z-3}{1}$ is:
  • a$(1, 2, -3)$
  • b$(-1, 2, 3)$
  • c$(1, -2, 3)$
  • d$(1, 2, 3)$

Answer

Answer

AI
Written by AI - it can contain mistakes.

Correct option: d

(d) $(1, 2, 3)$ The equations of the lines are $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$ and $\frac{x-1}{5} = \frac{y-2}{2} = \frac{z-3}{1}$. Substituting the point $(1, 2, 3)$ into both lines: For line 1: $\frac{1-1}{2} = \frac{2-2}{3} = \frac{3-3}{4} = 0$. For line 2: $\frac{1-1}{5} = \frac{2-2}{2} = \frac{3-3}{1} = 0$. Both lines pass through $(1, 2, 3)$, so their point of intersection is $(1, 2, 3)$.
Three-dimensional Geometry

From ISC 2027 Specimen Mathematics Paper 1, question 1(xii).

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