PU E 2026 Analytical Geometry in Three Dimensions Free Quiz 1

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PU E 2026 Analytical Geometry in Three Dimensions Free Quiz 1

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General 10 MCQs

1. What is the distance formula in 3D?

A. √[(x₂ - x₁)² + (y₂ - y₁)²] B. √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²] C. (x₂ - x₁) + (y₂ - y₁) + (z₂ - z₁) D. √[(x₂ - x₁)² - (y₂ - y₁)² + (z₂ - z₁)²]

2. What is the midpoint formula in 3D?

A. ((x₁+x₂)/2, (y₁+y₂)/2) B. (x₁+x₂, y₁+y₂, z₁+z₂) C. ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2) D. ((x₁-x₂)/2, (y₁-y₂)/2, (z₁-z₂)/2)

3. What is the distance between (1,2,3) and (4,6,8)?

A. 5 B. 7 C. √50 D. 5√2

4. What are direction ratios?

A. Direction ratios B. Direction cosines C. Angles D. Magnitudes

5. What are direction cosines?

A. Direction ratios B. Direction cosines C. Angles D. Slopes

6. What is the relation for direction cosines l, m, n?

A. l + m + n = 1 B. l² + m² + n² = 0 C. l² + m² + n² = 1 D. l × m × n = 1

7. What is the general equation of a plane?

A. ax + by + cz + d = 0 B. ax + by + cz = 0 C. ax² + by² + cz² + d = 0 D. ax + by = 0

8. What is the normal vector of 2x + 3y + 4z + 5 = 0?

A. (5, 0, 0) B. (2, 3, 4) C. (2, 3, 4, 5) D. (-2, -3, -4)

9. What is the distance from a point to a plane?

A. |ax₁ + by₁ + cz₁ + d| / (a + b + c) B. |ax₁ + by₁ + cz₁ + d| / √(a² + b²) C. |ax₁ + by₁ + cz₁ + d| / √(a² + b² + c²) D. |ax₁ + by₁ + cz₁ + d| / √(a² + b² + c² + d²)

10. What is the angle between two planes?

A. Angle between direction vectors B. Angle between position vectors C. Angle between lines D. Angle between normal vectors

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Chemistry: 20 MCQs
Physics: 20 MCQs
Quantitative Reasoning: 20 MCQs

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