Q1 · medium · AI-verified
If a line has direction cosines l = 1/√3, m = 1/√3, n = 1/√3, what angle does it make with the x-axis?
- 90°
- cos⁻¹(1/√3)
- 45°
- 30°
Q2 · medium · AI-verified
The line (x−1)/2 = (y+1)/3 = (z−0)/4 passes through which point?
- (2, 3, 4)
- (1, −1, 0)
- (−1, 1, 0)
- (0, 0, 0)
Q3 · medium · AI-verified
What is the distance between the parallel planes 2x − y + 3z = 4 and 2x − y + 3z = 10?
- 6/√7
- 3/√14
- 6/√14
- 6/√13
Q4 · medium · AI-verified
In three-dimensional geometry, the locus of a point equidistant from two fixed points A and B is:
- The perpendicular bisector plane of AB
- A line through the midpoint of AB
- A sphere with AB as diameter
- A circle centred at the midpoint of AB
Q5 · medium · AI-verified
Two lines are perpendicular if their direction ratios (a₁, b₁, c₁) and (a₂, b₂, c₂) satisfy:
- a₁a₂ + b₁b₂ + c₁c₂ = 1
- (a₁+a₂)² + (b₁+b₂)² + (c₁+c₂)² = 0
- a₁/a₂ = b₁/b₂ = c₁/c₂
- a₁a₂ + b₁b₂ + c₁c₂ = 0