Additional Mathematics 0606 / Vectors / 2.22.2: Finding constants and a unit vector0606/21/M/J/20 — Question 5 · 5 marksMark as done · Save for later · Show all solutionsThe vectors a\mathbf{a}a and b\mathbf{b}b are such that a=αi+j\mathbf{a} = \alpha\mathbf{i} + \mathbf{j}a=αi+j and b=12i+βj\mathbf{b} = 12\mathbf{i} + \beta\mathbf{j}b=12i+βj.(a)Find the value of each of the constants α\alphaα and β\betaβ such that 4a−b=(α+3)i−2j4\mathbf{a} - \mathbf{b} = (\alpha + 3)\mathbf{i} - 2\mathbf{j}4a−b=(α+3)i−2j.[3]▸ Answer(b)Hence find the unit vector in the direction of b−4a\mathbf{b} - 4\mathbf{a}b−4a.[2]▸ Answer▸ Official mark scheme← 1.7: Unit vectors, constants and collinear points2.11: Finding an intersection point with two parameters →
