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1.3 – Vectors and scalars
Description
Nature of science:
Models: First mentioned explicitly in a scientific paper in 1846, scalars and vectors reflected the work of scientists and mathematicians across the globe for over 300 years on representing measurements in three-dimensional space. (1.10)
Understandings:
- Vector and scalar quantities
- Combination and resolution of vectors
Applications and skills:
- Solving vector problems graphically and algebraically
Guidance:
- Resolution of vectors will be limited to two perpendicular directions
- Problems will be limited to addition and subtraction of vectors and the multiplication and division of vectors by scalars
Data booklet reference:
International-mindedness:
- Vector notation forms the basis of mapping across the globe
Theory of knowledge:
- What is the nature of certainty and proof in mathematics?
Utilization:
- Navigation and surveying (see Geography SL/HL syllabus: Geographic skills)
- Force and field strength (see Physics sub-topics 2.2, 5.1, 6.1 and 10.1)
- Vectors (see Mathematics HL sub-topic 4.1; Mathematics SL sub-topic 4.1)
Aims:
- Aim 2 and 3: this is a fundamental aspect of scientific language that allows for spatial representation and manipulation of abstract concepts.
Directly related questions
- 21M.1.SL.TZ1.1: Which lists one scalar and two vector quantities? A. Mass, momentum, potential difference B....
- 21M.1.SL.TZ1.1: Which lists one scalar and two vector quantities? A. Mass, momentum, potential difference B....
- 19N.1.SL.TZ0.2: An object is held in equilibrium by three forces of magnitude F, G and H that act at a point in...
- 19N.1.SL.TZ0.2: An object is held in equilibrium by three forces of magnitude F, G and H that act at a point in...
- 22N.1.HL.TZ0.5: The diagram shows the trajectory of a projectile and the velocity v of the projectile at point P...
- 22N.1.HL.TZ0.5: The diagram shows the trajectory of a projectile and the velocity v of the projectile at point P...
- 18M.1.SL.TZ1.2: A river flows north. A boat crosses the river so that it only moves in the direction east of its...
- 18M.1.SL.TZ1.2: A river flows north. A boat crosses the river so that it only moves in the direction east of its...
- 18M.1.SL.TZ2.2: The velocities vX and vY of two boats, X and Y, are shown. Which arrow represents the...
- 18M.1.SL.TZ2.2: The velocities vX and vY of two boats, X and Y, are shown. Which arrow represents the...
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18M.2.SL.TZ2.1a.ii:
On the diagram, construct an arrow of the correct length to represent the weight of the ball.
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18M.2.SL.TZ2.1a.ii:
On the diagram, construct an arrow of the correct length to represent the weight of the ball.
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18M.2.SL.TZ2.a.ii:
On the diagram, construct an arrow of the correct length to represent the weight of the ball.
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18M.2.HL.TZ2.1a.ii:
On the diagram, construct an arrow of the correct length to represent the weight of the ball.
-
18M.2.HL.TZ2.1a.ii:
On the diagram, construct an arrow of the correct length to represent the weight of the ball.
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18M.2.HL.TZ2.a.ii:
On the diagram, construct an arrow of the correct length to represent the weight of the ball.
- 18N.1.SL.TZ0.21: Two parallel wires are perpendicular to the page. The wires carry equal currents in opposite...
- 18N.1.SL.TZ0.21: Two parallel wires are perpendicular to the page. The wires carry equal currents in opposite...
- 19M.2.HL.TZ2.1c: A student models the bounce of the tennis ball to predict the angle θ at which the ball leaves a...
- 19M.2.HL.TZ2.1c: A student models the bounce of the tennis ball to predict the angle θ at which the ball leaves a...
- 19M.2.HL.TZ2.c: A student models the bounce of the tennis ball to predict the angle θ at which the ball leaves a...
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19M.2.SL.TZ1.1b.i:
Calculate the component of weight for the bicycle and girl acting down the slope.
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19M.2.SL.TZ1.1b.i:
Calculate the component of weight for the bicycle and girl acting down the slope.
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19M.2.SL.TZ1.b.i:
Calculate the component of weight for the bicycle and girl acting down the slope.
- 19M.2.SL.TZ2.1c: The student models the bounce of the tennis ball to predict the angle θ at which the ball leaves...
- 19M.2.SL.TZ2.c: The student models the bounce of the tennis ball to predict the angle θ at which the ball leaves...
- 19M.2.SL.TZ2.1c: The student models the bounce of the tennis ball to predict the angle θ at which the ball leaves...
- 20N.1.SL.TZ0.2: A list of four physical quantities is acceleration energy mass temperature How many...
- 20N.1.SL.TZ0.2: A list of four physical quantities is acceleration energy mass temperature How many...
- 21N.1.SL.TZ0.1: Which is a vector quantity? A. Acceleration B. Energy C. Pressure D. Speed
- 21N.1.SL.TZ0.1: Which is a vector quantity? A. Acceleration B. Energy C. Pressure D. Speed
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22M.1.SL.TZ1.2:
The magnitude of the resultant of two forces acting on a body is 12 N. Which pair of forces acting on the body can combine to produce this resultant?
A. 1 N and 2 N
B. 1 N and 14 N
C. 5 N and 6 N
D. 6 N and 7 N
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22M.1.SL.TZ1.2:
The magnitude of the resultant of two forces acting on a body is 12 N. Which pair of forces acting on the body can combine to produce this resultant?
A. 1 N and 2 N
B. 1 N and 14 N
C. 5 N and 6 N
D. 6 N and 7 N
- 22M.2.SL.TZ1.1a: Outline two differences between the momentum of the box and the momentum of the load at the same...
- 22M.2.SL.TZ1.1a: Outline two differences between the momentum of the box and the momentum of the load at the same...
- 22M.2.SL.TZ1.a: Outline two differences between the momentum of the box and the momentum of the load at the same...
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22M.1.HL.TZ2.16:
Four particles, two of charge +Q and two of charge −Q, are positioned on the -axis as shown. A particle P with a positive charge is placed on the -axis. What is the direction of the net electrostatic force on this particle?
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22M.1.HL.TZ2.16:
Four particles, two of charge +Q and two of charge −Q, are positioned on the -axis as shown. A particle P with a positive charge is placed on the -axis. What is the direction of the net electrostatic force on this particle?
- 22N.1.SL.TZ0.2: Two forces, F and G, act on a system. F is reversed in direction and G is halved. Which...
- 22N.1.SL.TZ0.2: Two forces, F and G, act on a system. F is reversed in direction and G is halved. Which...
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22N.1.SL.TZ0.4:
A projectile is launched with a velocity at an angle to the horizontal. It reaches a maximum height . What is the time taken to reach the maximum height?
A.B.
C.
D.
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22N.1.SL.TZ0.4:
A projectile is launched with a velocity at an angle to the horizontal. It reaches a maximum height . What is the time taken to reach the maximum height?
A.B.
C.
D.
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22N.2.SL.TZ0.4a:
The scale diagram shows the weight W of the mass at an instant when the rod is horizontal.
Draw, on the scale diagram, an arrow to represent the force exerted on the mass by the rod.
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22N.2.SL.TZ0.4a:
The scale diagram shows the weight W of the mass at an instant when the rod is horizontal.
Draw, on the scale diagram, an arrow to represent the force exerted on the mass by the rod.
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22N.2.SL.TZ0.a:
The scale diagram shows the weight W of the mass at an instant when the rod is horizontal.
Draw, on the scale diagram, an arrow to represent the force exerted on the mass by the rod.