Additional Mathematics 0606 / Vectors / 1.31.3: Column vectors: equal moduli and comparing components0606/12/M/J/16 — Question 3 · 6 marksMark as done · Save for later · Show all solutionsVectors a\mathbf{a}a, b\mathbf{b}b and c\mathbf{c}c are such that a=(2y)\mathbf{a} = \begin{pmatrix} 2 \\ y \end{pmatrix}a=(2y), b=(13)\mathbf{b} = \begin{pmatrix} 1 \\ 3 \end{pmatrix}b=(13) and c=(−55)\mathbf{c} = \begin{pmatrix} -5 \\ 5 \end{pmatrix}c=(−55).(i)Given that ∣a∣=∣b−c∣|\mathbf{a}| = |\mathbf{b} - \mathbf{c}|∣a∣=∣b−c∣, find the possible values of yyy.[3]▸ Answer(ii)Given that μ(b+c)+4(b−c)=λ(2b−c)\mu(\mathbf{b} + \mathbf{c}) + 4(\mathbf{b} - \mathbf{c}) = \lambda(2\mathbf{b} - \mathbf{c})μ(b+c)+4(b−c)=λ(2b−c), find the value of μ\muμ and of λ\lambdaλ.[3]▸ Answer▸ Official mark scheme← 2.8: Column vectors and a point dividing a segment2.1: Collinear points and a unit vector →
