Mathematics for IGCSE & O level - Vectors (Section 1 - No. 14)
Given the vectors \(\vec{u} = \begin{pmatrix} 1 \\ 0 \end{pmatrix}\) and \(\vec{v} = \begin{pmatrix} 0 \\ 1 \end{pmatrix}\), which of the following are true?
The magnitude of \(\vec{u}\) is 1.
The magnitude of \(\vec{v}\) is 0.
\(\vec{u}\) and \(\vec{v}\) are perpendicular.
\(\vec{u} + \vec{v} = \begin{pmatrix} 1 \\ 1 \end{pmatrix}\)
Explanation
Magnitude of u = sqrt(1^2 + 0^2) = 1. Magnitude of v = sqrt(0^2 + 1^2) = 1. u+v = (1,1). They are perpendicular.
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