Mathematics for IGCSE & O level - Vectors (Section 1 - No. 45)
Considering the magnitude of vectors, which of the following statements are correct?
The magnitude of \(\begin{pmatrix} 3 \\ 4 \end{pmatrix}\) is 5.
The magnitude of -\(\begin{pmatrix} 3 \\ 4 \end{pmatrix}\) is -5
The magnitude of a vector is always positive.
The magnitude is found using the Pythagorean theorem.
Explanation
The magnitude is calculated as the square root of the sum of squares of the components, therefore \(\sqrt{3^2 + 4^2}\) = 5. It's always positive. The magnitude of -\(\begin{pmatrix} 3 \\ 4 \end{pmatrix}\) is \(\sqrt{(-3)^2 + (-4)^2}\) = 5. The Pythagorean theorem is used.