Vectors, Components and Addition
A vector has magnitude and direction, is written in component form as a i + b j + c k, and adds component-wise.
What is Vectors, Components and Addition?
A vector has magnitude and direction, is written in component form as a i + b j + c k, and adds component-wise.
Key formula / rule: Magnitude is √(a2 + b2 + c2).
Key points
- Compute the magnitude and unit vector of a given vector.
- Apply the section formula using position vectors.
Common exam trap
Adding magnitudes instead of adding components.
Definitions
- Term
Vectors, Components and Addition
- Meaning
A vector has magnitude and direction, is written in component form as a i + b j + c k, and adds component-wise.
- Term
Vectors, Components and Addition — explanation
- Meaning
Resolving into components turns geometry into arithmetic, and the unit vector along any non-zero vector is obtained by dividing by its magnitude. Position vectors let points and directions be handled with the same algebra.
Learning objectives
Compute the magnitude and unit vector of a given vector.
Apply the section formula using position vectors.
Formulae
- Key point
Magnitude is √(a2 + b2 + c2).
- Key point
The unit vector is the vector divided by its magnitude.
- Key point
The section formula gives the position vector of a dividing point.
Common mistakes
Adding magnitudes instead of adding components.
Treating a position vector and a direction vector as interchangeable.
Keywords
Vectors
Components
Addition
Practice preview
If vector A = 2i + 3j - k and vector B = i - 2j + 3k, what is A + B?…
easy
The magnitude of the vector V = 3i - 4j + 5k is:…
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Find the unit vector in the direction of the vector A = 6i - 8j.…
medium