Relative to a fixed origin OOO, the lines l1l_1l1 and l2l_2l2 are given by the equations
l1:r=(2i+pj+5k)+λ(3i−j+2k)l_1: \mathbf{r} = (2\mathbf{i} + p\mathbf{j} + 5\mathbf{k}) + \lambda(3\mathbf{i} - \mathbf{j} + 2\mathbf{k})l1:r=(2i+pj+5k)+λ(3i−j+2k) l2:r=(1i+3j+4k)+μ(2i+4j+k)l_2: \mathbf{r} = (1\mathbf{i} + 3\mathbf{j} + 4\mathbf{k}) + \mu(2\mathbf{i} + 4\mathbf{j} + \mathbf{k})l2:r=(1i+3j+4k)+μ(2i+4j+k)
where λ\lambdaλ and μ\muμ are scalar parameters and ppp is a constant.
Given that l1l_1l1 and l2l_2l2 intersect,
find the value of ppp.
find the position vector of the point of intersection.
Find the acute angle between l1l_1l1 and l2l_2l2. Give your answer in degrees to one decimal place.
The point AAA lies on l1l_1l1 with parameter λ=1\lambda = 1λ=1. The point BBB lies on l2l_2l2 with AB⃗\vec{AB}AB perpendicular to l2l_2l2.
Find the coordinates of BBB.
Practise Edexcel A Level Maths Vectors with exam-style questions for A Level Maths. 100 questions covering 12.1 3D Coordinates, 12.2 Vectors in 3D, 12.3 Solving Geometric Problems, and 12.4 Application to Mechanics, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.