GCSE Maths Practice: vectors
This question teaches scalar multiplication of vectors.
Multiply each component by the scalar individually. Check signs carefully.
Scalar multiplication involves multiplying every component of a vector by a scalar (a number). For example, multiplying \(\begin{pmatrix}3\\-1\end{pmatrix}\) by 2: multiply the top component: 2*3=6, and the bottom component: 2*(-1)=-2, giving \(\begin{pmatrix}6\\-2\end{pmatrix}\). This changes the magnitude of the vector while keeping the direction the same if the scalar is positive; a negative scalar also reverses direction. Scalar multiplication is used in physics for scaling forces, velocities, or displacements. Understanding how to scale vectors is essential for vector algebra, transformations, and problem-solving. Practice with positive, negative, and fractional scalars to build confidence. Visualization on a grid helps see how the vector stretches or reverses with the scalar. Combining scalar multiplication with vector addition allows solving more complex problems like resultant displacements or forces.