CAIE A-Level Mathematics A2 3.7.5 Whether Two Lines Are Parallel Questions
Practise analysing parallel, intersecting and skew lines using vector equations.
- Syllabus
- 2028–2030
- Course
- Mathematics 9709
- Level
- A2
Exam points
- classify lines as parallel, intersecting or skew
- find intersections and parameters from vector equations
- solve geometric conditions involving vector lines
CAIE A-Level Mathematics A2 3.7.5 Whether Two Lines Are Parallel Questions question 1
[Maximum number: 5]
9 Two lines l and m have equations r=3 i+2 j+5 k+s(4 i-j+3 k) and r=i-j-2 k+t(-i+2 j+2 k) respectively.
Show that l and m intersect and state the position vector of the point of intersection.
Express general point of l or m in component form,
e.g. (3+4 s, 2-s, 5+3 s) or (1-t,-1+2 t,-2+2 t)
Equate at least two pairs of components and solve for s or for t
Obtain correct answer s=-1 and t=2
Verify that all three equations are satisfied
State position vector of the intersection -i+3 j+2 k, or equivalent
Can come from 1 correct value and no contradictory
statement.
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