Lesson 10.4.1
10.4.1 Position vectors and the distance between points Quiz: Pearson Edexcel Maths, Unit 10
20 questions
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Lesson 10.4.1, Position vectors and the distance between points: 20 multiple choice questions for the Pearson Edexcel Maths (9MA0), Unit 10: Vectors, written with Revision Ninja.
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The 20 questions
-
What is the position vector of point A relative to origin O?
- OA
- AB
- AO
- BO
-
How is the position vector of point P with coordinates (3, 4, -5) written in column form?
- (4, 3, -5)^T
- (3, 4, -5)^T
- (3, 4, 5)^T
- (-3, -4, 5)^T
-
Given position vectors a and b for points A and B, what vector represents AB?
- a - b
- 0.5(a + b)
- b - a
- a + b
-
What formula calculates the magnitude of a 3D vector with components x, y, and z?
- sqrt(x^2 + y^2 + z^2)
- sqrt(x + y + z)
- x + y + z
- x^2 + y^2 + z^2
-
What is the distance between points with position vectors a and b?
- |b - a|
- b - a
- |a + b|
- |a| - |b|
-
What is the distance between the origin and the point with position vector (2, -3, 6)?
- 11
- 7
- sqrt(35)
- 5
-
What term describes a vector with a magnitude of exactly one unit?
- Position vector
- Direction vector
- Unit vector
- Zero vector
-
How do you find a unit vector in the direction of vector a?
- |a| / a
- a / |a|
- a - |a|
- a * |a|
-
Find the vector AB if position vector A is (1, 2, 3) and B is (4, 6, 3).
- (-3, -4, 0)
- (3, 4, 0)
- (5, 8, 6)
- (3, 4, 6)
-
What is the exact distance between points (1, 2, 3) and (4, 6, 3)?
- 7
- sqrt(7)
- 25
- 5
-
Which vector represents the origin in a three-dimensional coordinate system?
- (1, 1, 1)
- (0, 0, 1)
- (0, 0, 0)
- (-1, -1, -1)
-
What is the magnitude of the position vector (3, 0, -4)?
- sqrt(7)
- 1
- 7
- 5
-
If vector AB = (2, -2, 1), what is the length of segment AB?
- 5
- sqrt(5)
- 9
- 3
-
What is the midpoint of the line segment joining position vectors a and b?
- a - b
- 2(a + b)
- b - a
- 0.5(a + b)
-
Find the midpoint between points (2, 4, 6) and (4, 2, 0).
- (3, 3, 3)
- (6, 6, 6)
- (1, 1, -3)
- (2, 1, 0)
-
Two points have position vectors a and b. When does |a - b| equal zero?
- a is parallel to b
- a is perpendicular to b
- a equals b
- a + b equals 0
-
What is the unit vector in the direction of (0, 3, 4)?
- (0, 0.6, 0.8)
- (0, 3/5, 4/5)
- (0, 0.3, 0.4)
- (0, 3, 4)
-
If point P has position vector p, what does |-p| equal?
- -|p|
- |p|
- 2|p|
- 0
-
What geometric shape has all points equidistant from a fixed position vector centre?
- Sphere
- Cube
- Cylinder
- Circle
-
What is the radius of a sphere given by the equation of distance from centre c?
- Scalar product
- Midpoint
- Magnitude
- Direction
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