The point of intersection of the lines and is:
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
AIWritten 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 $(1, 2, 3)$.
From ISC 2027 Specimen Mathematics Paper 1, question 1(xii).