| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/1 (Pre-U Mathematics Paper 1) |
| Year | 2013 |
| Session | June |
| Marks | 6 |
| Topic | Vectors 3D & Lines |
| Type | Find intersection point given lines are known to intersect |
| Difficulty | Standard +0.3 This is a straightforward application of the standard method for finding line intersections in 3D: set parameters equal and solve the resulting system. While it requires careful algebraic manipulation across three equations, it's a routine textbook exercise with no conceptual difficulty or novel insight required—slightly easier than average due to its mechanical nature. |
| Spec | 4.04a Line equations: 2D and 3D, cartesian and vector forms |
Attempt to equate at least two of:
$5 + 4\lambda = 9 - 2\mu$
$11 + 3\lambda = 4 + \mu$
$7 - 5\lambda = -4 + 4\mu$ — M1
Obtain at least two correct — A1
Attempt to solve two equations — M1*
Obtain $\lambda = -1$, $\mu = 4$ — A1
Attempt to substitute *their* value for $\lambda$ or $\mu$ — M1*
Obtain $(1, 8, 12)$ — A1 **[6]**10 Two intersecting straight lines have equations
$$\frac { x - 5 } { 4 } = \frac { y - 11 } { 3 } = \frac { z - 7 } { - 5 } \quad \text { and } \quad \frac { x - 9 } { - 2 } = \frac { y - 4 } { 1 } = \frac { z + 4 } { 4 } .$$
Find the coordinates of their point of intersection.
\hfill \mbox{\textit{Pre-U Pre-U 9794/1 2013 Q10 [6]}}