Specialist Mathematics Β· Unit 3 Β· Vectors in two and three dimensions Β· Vectors in three dimensions
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Consider the vector \(\mathbf{p} = 3\mathbf{i} - 4\mathbf{j} + 12\mathbf{k}\). (a) Calculate \(|\mathbf{p}|\). (1 mark) (b) Hence, determine the magnitude of the vector \(2\mathbf{p}\). (1 mark)
A drone flies from base point B to observation point C. The displacement vector BC is given by BC = 4i - 3j + 12k, where distances are measured in metres. Calculate the magnitude |BC| and express your answer in metres.
Vector \(\mathbf{p}\) has initial point \(A(2, -1, 4)\) and terminal point \(B(5, 3, -2)\), as shown in the diagram. Calculate \(|\mathbf{p}|\).