scalar multiplication
What scalar multiplication means in Mathematics A-Level, as defined for AQA, Pearson Edexcel, WJEC.
Definitions of scalar multiplication
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Reference: WJEC
Multiplication by a scalar k scales the vector's magnitude by |k|: k(xi + yj) = (kx)i + (ky)j, with direction unchanged if k > 0 and reversed if k < 0.
Multiplying by scalar k scales every component, so k(a, b) = (ka, kb), with magnitude scaling by |k| and direction reversing when k is negative.
Multiplying by a scalar k stretches the vector by factor k, and if k is negative the direction reverses.
Topics that use scalar multiplication
- J: Vectors (AQA A-Level)
- Vectors (Pearson Edexcel A-Level)
- Vectors (AS Unit 1: Pure Mathematics A) (WJEC A-Level)
Related terms
- Parallel vectors
- Position vector
- component
- component form
- direction
- Displacement vector
- Magnitude
- magnitude/direction form
Using scalar multiplication in the exam
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