It is given that v=6i−2j+3k\mathbf{v} = 6\mathbf{i} - 2\mathbf{j} + 3\mathbf{k}v=6i−2j+3k.
Find ∣v∣\left|\mathbf{v}\right|∣v∣.
Find a unit vector in the direction of v\mathbf{v}v.
The vector w=ci−4j+6k\mathbf{w} = c\mathbf{i} - 4\mathbf{j} + 6\mathbf{k}w=ci−4j+6k is parallel to v\mathbf{v}v, where c c\,c is a constant.
Find the value of c c\,c and the value of ∣w∣\left|\mathbf{w}\right|∣w∣.
168 exam-style questions on OCR (MEI) A Level Maths 1.11 Vectors, covering 1.11.1 Language of vectors in two dimensions, 1.11.2 Add, subtract and scale vectors, 1.11.3 Magnitude and direction of a vector, 1.11.4 Position vectors, 1.11.5 Distance between points by position vectors, 1.11.6 Vectors to solve problems, 1.11.7 Language of vectors in three dimensions (A-level only), and 1.11 Vectors. Each one has a worked solution and a mark scheme showing where the marks go.