Topic 7 of 9 · Form 4
Vectors in two dimensions
Column vectors and i, j notation; magnitude |xi + yj| = √(x² + y²); unit vectors; position vectors; parallel vectors are multiples of each other.
Notes for this topic 1 file, in order
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Vector notation
Column vectors and i, j notation; magnitude |xi + yj| = √(x² + y²); unit vectors; position vectors; parallel vectors are multiples of each other.
Vector geometry
Express vectors in terms of given vectors; ratio theorem; show points are collinear.
Worked example: OA = 2i + 3j and OB = 6i − j. Find AB and its magnitude.
AB = OB − OA = 4i − 4j; |AB| = √32 = 4√2
Velocity and displacement
Position = initial position + velocity × time (r = r₀ + vt). Relative velocity and finding when two objects meet or are a given distance apart.
Worked example: A boat starts at (2i + j) km and moves with velocity (3i + 4j) km/h. Find its position after 2 hours and its speed.
r = (2i + j) + 2(3i + 4j) = 8i + 9j; speed = |3i + 4j| = 5 km/h
Check yourself
- Find a unit vector in the direction of 5i − 12j.
- Are 2i − 3j and −6i + 9j parallel?
- Find |−8i + 6j|.
Show answers
- (5i − 12j)/13
- Yes (−3 times the first).
- 10
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