GCSE Maths Practice: vectors

Question 4 of 10

This question teaches scalar multiplication of vectors.

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\( \begin{array}{l}\text{Find } 3\mathbf{a} \text{ if } \mathbf{a} = \begin{pmatrix}2\\-1\end{pmatrix}.\end{array} \)

Choose one option:

Multiply each component separately. Check the signs carefully.

Scalar multiplication involves multiplying every component of a vector by a scalar. For example, multiplying \(\mathbf{a} = \begin{pmatrix}2\\-1\end{pmatrix}\) by 3 gives the top component 2*3=6 and the bottom -1*3=-3, resulting in \(\begin{pmatrix}6\\-3\end{pmatrix}\). Scalar multiplication changes the vector's magnitude but not direction if the scalar is positive. Negative scalars reverse direction, and zero produces the zero vector. Understanding this operation is essential in physics, navigation, and coordinate geometry, especially for displacement, forces, and motion problems. Practice with positive, negative, and zero scalars to visualize the effect on vectors and gain confidence in computations.