2.1-2.2
Your guide: Sir HamzaBelieves every formula has a story, and units never lie.
Some answers need a number. Others need a number and a direction.
Let us learn to tell them apart, and to split a vector in two.
Smart Syllabus 2026 leaves out sections 2.1 and 2.2 for the 2026 exam. Read them for understanding, because the rest of the chapter uses vectors.
A scalar has only magnitude. Examples: mass, distance, speed, time, energy and temperature.
A vector needs magnitude and direction. Examples: displacement, velocity, acceleration and force.
A vector is drawn as an arrow. The length shows magnitude. The head shows direction.
In print, a vector is a bold letter such as V or F, or a letter with an arrow above it.
A component is the effective value of a vector in a given direction.
Rectangular components lie along two perpendicular directions.
Take A at angle θ to the x-axis. Then A = Aₓ + A_y (Eq. 2.1).
The magnitudes are Aₓ = A cos θ (Eq. 2.2) and A_y = A sin θ (Eq. 2.3).
Use Pythagoras. A2 = Aₓ2 + A_y2, so A = √(Aₓ2 + A_y2) (Eq. 2.4).
The direction: tan θ = A_y ÷ Aₓ, so θ = tan−1(A_y ÷ Aₓ) (Eq. 2.5).
Book Example 2.1 uses these to find the angle between two equal forces with an equal resultant: 120°.
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Some answers need a number. Others need a number and a direction.
Let us learn to tell them apart, and to split a vector in two.
Smart Syllabus 2026 leaves out sections 2.1 and 2.2 for the 2026 exam. Read them for understanding, because the rest of the chapter uses vectors.
A scalar has only magnitude. Examples: mass, distance, speed, time, energy and temperature.
A vector needs magnitude and direction. Examples: displacement, velocity, acceleration and force.
A vector is drawn as an arrow. The length shows magnitude. The head shows direction.
In print, a vector is a bold letter such as V or F, or a letter with an arrow above it.
A component is the effective value of a vector in a given direction.
Rectangular components lie along two perpendicular directions.
Take A at angle θ to the x-axis. Then A = Aₓ + A_y (Eq. 2.1).
The magnitudes are Aₓ = A cos θ (Eq. 2.2) and A_y = A sin θ (Eq. 2.3).
Use Pythagoras. A2 = Aₓ2 + A_y2, so A = √(Aₓ2 + A_y2) (Eq. 2.4).
The direction: tan θ = A_y ÷ Aₓ, so θ = tan−1(A_y ÷ Aₓ) (Eq. 2.5).
Book Example 2.1 uses these to find the angle between two equal forces with an equal resultant: 120°.
Q1. Book Example 2.1: find the angle between two equal forces whose resultant equals each of them.
Rₓ = F + F cos θ, R_y = F sin θ. F2 = Rₓ2 + R_y2 gives 0 = F2(2 cos θ + 1). So cos θ = −0.5 and θ = 120°.
✗ “Speed is a vector.”
✓ Speed has no direction. The book lists it as a scalar. Velocity is the vector.
✗ “Aₓ = A sin θ.”
✓ With θ from the x-axis, Aₓ = A cos θ. A_y uses sin.
1. Which is a vector?
(c) Displacement has magnitude and direction.
2. The x-component of A at angle θ is:
(a) Eq. 2.2.
3. Which formula gives the direction from components?
(a) Eq. 2.5.
4. The resultant of two equal forces equals each force. The angle between them is:
(c) Book Example 2.1.
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