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Part 1: Addition and Subtraction of Coplanar vectors
Two vectors are added or subtracted using the ‘triangle law’:
Part 2: Multiplication of a Vector by a Scalar
Type 1: k = 1
The vector -a has the same magnitude as the vector a but is in the opposite direction.
Type 2: k > 1
Type 3: k < 1
In geometry, magnitude of a vector means the distance of the vector.
To find the magnitude of a vector, use Pythagoras’ Theorem.
The position vector of a point A is the vector OA, where O is the origin. OA is usually written as a vector a.
The position of A and B, AB = b – a
A unit vector is a vector which has magnitude 1 unit.
If λa + µb = αa + βb are not parallel, then λ = α and µ = β.
Proof 1: Parallel Line
Condition: If AB = k CD, AB and CD are parallel.
For example, 6a + 3b is parallel to 2a + b, since 6a + 3b = 3 x (2a + b)
Proof 2: Straight Line
Condition 1: If AB = k CD, AB and CD are parallel.
Condition 2: Since both AB and BC go through common point B, therefore ABC is a straight line.
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