Equations of Lines in 3D (Cartesian & Vector form)

Grade 12 Maths Higher — Equations of Lines in 3D (Cartesian & Vector form): 25 practice questions with instant scoring and explanations.

1. Vector form of line passing through a with direction b: r =
2. Parametric form of line r = a + tb gives:
3. Cartesian form of line through (x₁, y₁, z₁) with direction ratios (a, b, c):
4. Line through (1, 2, 3) with direction (1, -1, 2) has Cartesian form:
5. Line passing through points A(1, 2, 3) and B(4, 5, 6):
6. Condition for two lines r = a₁ + t·b₁ and r = a₂ + s·b₂ to be parallel:
7. Condition for two lines to be perpendicular:
8. Two skew lines are:
9. Distance between point P and line r = a + tb is:
10. Distance between two parallel lines r = a₁ + t·b and r = a₂ + t·b:
11. Distance between two skew lines requires:
12. Shortest distance between skew lines: d = |[(a₂-a₁)·(b₁ × b₂)]|/|b₁ × b₂|
13. A line perpendicular to plane x + 2y - z = 0 has direction ratios:
14. Foot of perpendicular from P to line r = a + tb is found by:
15. Line r = (2,3,4) + t(1,2,3) passes through point:
16. Angle θ between lines with direction vectors b₁ and b₂ is:
17. Two lines are coplanar if scalar triple product [(a₂-a₁)·(b₁ × b₂)] =
18. Symmetric form (x-1)/2 = (y+3)/(-1) = (z-2)/3 represents:
19. If line (x-a)/l = (y-b)/m = (z-c)/n = k, then point on line is:
20. Equations of coordinate axes:
21. A line in the xy-plane satisfies:
22. Lines (x-1)/1 = (y-2)/2 = (z-3)/3 and (x-4)/1 = (y-5)/2 = (z-6)/3 are:
23. Point of intersection (if exists) of two lines found by:
24. For line r = (1,2,3) + t(1,1,1), when does it pass through (2,3,4)?
25. Review question for Equations of Lines in 3D (Cartesian & Vector form)