Mathematics for IGCSE & O level - Vectors (Section 2 - No. 10)
Given \( ec{a} = egin{pmatrix} 1 \\ 2 \end{pmatrix}\) and \( ec{b} = egin{pmatrix} 3 \\ -1 \end{pmatrix}\), which of the following is/are true about the vector 2\(\vec{a}\) + \(\vec{b}\)?
It is equal to \( egin{pmatrix} 5 \\ 3 \end{pmatrix}\)
Its magnitude is \(\sqrt{34}\)
It is a linear combination of \(\vec{a}\) and \(\vec{b}\)
It has a slope of \(\frac{1}{3}\)
Explanation
2a + b = 2\(\begin{pmatrix} 1 \\ 2 \end{pmatrix}\) + \(\begin{pmatrix} 3 \\ -1 \end{pmatrix}\) = \(\begin{pmatrix} 2 \\ 4 \end{pmatrix}\) + \(\begin{pmatrix} 3 \\ -1 \end{pmatrix}\) = \(\begin{pmatrix} 5 \\ 3 \end{pmatrix}\). The magnitude is \(\sqrt{5^2 + 3^2}\) = \(\sqrt{34}\). Because the vector 2a + b is calculated from a and b, it is a linear combination of a and b.
Comments (0)
