GCSE Maths Practice: vectors

Question 10 of 10

This question explains the effects of scalar multiplication on vectors.

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\( \begin{array}{l}\text{Which statements are true about scalar multiplication of vectors?}\end{array} \)

Select all correct options:

Check the sign of the scalar: positive → same direction, negative → reverse, zero → zero vector.

Scalar multiplication alters a vector's magnitude and can change its direction depending on the scalar. Multiplying by a positive scalar stretches the vector, increasing its length but maintaining the same direction. Multiplying by zero produces the zero vector, which has no magnitude and no direction. Multiplying by a negative scalar reverses the vector's direction while scaling its length. Understanding these effects is crucial for geometry, physics, and engineering, especially when analyzing forces, motion, or translations. Practicing scalar multiplication with various positive, negative, and zero values helps students predict vector behavior and ensures correct component-wise calculations. Visualization on a coordinate grid strengthens comprehension, allowing learners to see how vectors stretch, shrink, or reverse with scalar changes.