Distance of Point from Plane, Angle between Lines/Planes

Grade 12 Maths Higher — Distance of Point from Plane, Angle between Lines/Planes: 25 practice questions with instant scoring and explanations.

1. Distance from (1, 1, 1) to plane x + y + z - 3 = 0:
2. Distance from (1, 0, 0) to plane 3x + 4y + 0z - 6 = 0:
3. Perpendicular distance uses formula with ____ in numerator:
4. Angle between line and plane is:
5. Line r = a + tb with direction b and plane with normal n: sin(θ) =
6. Line parallel to plane means:
7. Line perpendicular to plane means:
8. Distance between two skew lines with scalar triple product:
9. Acute angle between two planes:
10. Lines L₁: r = a₁ + td₁ and L₂: r = a₂ + sd₂ skew if:
11. Common perpendicular to two skew lines:
12. Projection of line onto plane: foot point satisfies:
13. Angle between line (x-1)/2 = (y-0)/1 = (z-1)/-1 and plane x + y - z = 1:
14. Distance from point (2, 3, 4) to plane 2x + 3y + 6z - 10 = 0:
15. Angle between planes x + y + z = 1 and x - y + z = 2:
16. Bisector planes of two planes P₁ and P₂:
17. Image of point in plane:
18. Line intersects plane if:
19. Foot of perpendicular from (1,2,3) to plane x + y + z = 6:
20. Angle between vectors (1,0,1) and plane containing (0,1,0) and (0,0,1):
21. Distance from origin to plane 2x - 3y + 6z = 14:
22. Two planes with normals n₁, n₂: angle bisector normal =
23. Angle between line in direction (1,2,3) and plane with normal (1,-1,0):
24. Common perpendicular of skew lines is:
25. Distance of point (1, 2, 3) from plane x + y + z = 6: