Specialist Mathematics · Unit 1 · Vectors in the plane · Representing vectors in the plane by directed line segments
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Consider the vectors $\vec{a} = (2k - 3)\vec{i} + (k + 5)\vec{j} + 4\vec{k}$ and $\vec{b} = 5\vec{i} + 8\vec{j} + (3k - 2)\vec{k}$, where $k$ is a constant. a) Determine the value of $k$ for which $\vec{a} = \vec{b}$. (2 marks) b) Hence determine the vector $\vec{a}$ when $\vec{a} = \vec{b}$. (1 mark)
Given that vectors **a** = (2k + 1)**i** + (3 − k)**j** + 4**k** and **b** = 7**i** + m**j** + 4**k** are equal, determine the values of k and m.
Given vectors $\mathbf{a} = 3\mathbf{i} - 2\mathbf{j} + 5\mathbf{k}$ and $\mathbf{b} = m\mathbf{i} + n\mathbf{j} + 5\mathbf{k}$, where $\mathbf{a} = \mathbf{b}$, determine the value of $m + n$.
Use the information in the table to determine all real values of $k$ for which vectors $\mathbf{u}$ and $\mathbf{v}$ are equal. If no such value exists, state this and explain why.