GCSE Maths Practice: vectors

Question 7 of 10

This question teaches scalar multiplication by a negative number.

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\( \begin{array}{l}\text{What is } -2 \times \begin{pmatrix}1\\-3\end{pmatrix}?\end{array} \)

Choose one option:

Multiply each component separately; negative scalar reverses direction.

Multiplying a vector by a scalar affects its magnitude and possibly its direction. A positive scalar stretches the vector, a negative scalar reverses it, and zero produces the zero vector. For \(\mathbf{v} = \begin{pmatrix}1\\-3\end{pmatrix}\) multiplied by -2: top = 1*-2=-2, bottom=-3*-2=6, resulting in \(\begin{pmatrix}-2\\6\end{pmatrix}\). Understanding negative scalar multiplication is essential for vector transformations, displacement analysis, and physics problems. Visualizing the effect on a graph reinforces understanding and prevents mistakes in direction and magnitude calculations.