A high-precision calibration glider of mass 0.4 kg is being manipulated on a horizontal low-friction air-table. Two magnetic actuators exert forces F1\mathbf{F}_1F1 and F2\mathbf{F}_2F2 on the glider, where:
F1=[2a1.8] N and F2=[−3b] N \mathbf{F}_1 = \begin{bmatrix} 2a \\ 1.8 \end{bmatrix} \text{ N and } \mathbf{F}_2 = \begin{bmatrix} -3 \\ b \end{bmatrix} \text{ N} F1=[2a1.8] N and F2=[−3b] Nand a,b a, b\,a,b are constants. The glider's resulting acceleration vector is given by a=[5b10a] m s−2\mathbf{a} = \begin{bmatrix} 5b \\ 10a \end{bmatrix} \text{ m s}^{-2}a=[5b10a] m s−2.
Determine the value of a a\,a and the value of bbb.
197 exam-style questions on OCR A Level Maths 1.10 Vectors, covering 1.10.1 Vectors in two dimensions, 1.10.2 Vectors in three dimensions (A-level only), 1.10.3 Magnitude and direction of vectors, 1.10.4 Basic operations on vectors, 1.10.5 Position vectors, 1.10.6 Distance between points, 1.10.7 Problem solving using vectors, 1.10.8 Vectors in kinematics, and 1.10 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.