The vectors a=2i−j+4k\mathbf{a}=2\mathbf{i}-\mathbf{j}+4\mathbf{k}a=2i−j+4k and b=−3i+5j+pk\mathbf{b}=-3\mathbf{i}+5\mathbf{j}+p\mathbf{k}b=−3i+5j+pk have resultant r=a+b\mathbf{r}=\mathbf{a}+\mathbf{b}r=a+b.
Given that ∣r∣=42|\mathbf{r}|=\sqrt{42}∣r∣=42, find the two possible values of ppp.
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.