The points A A\,A and B B\,B have position vectors
a=2i+pj−k\mathbf{a} = 2\mathbf{i} + p\mathbf{j} - \mathbf{k}a=2i+pj−k and b=6i+3j+qk\mathbf{b} = 6\mathbf{i} + 3\mathbf{j} + q\mathbf{k}b=6i+3j+qk
where p p\,p and q q\,q are constants. The point C C\,C has position vector c=14i−3j+11k\mathbf{c} = 14\mathbf{i} - 3\mathbf{j} + 11\mathbf{k}c=14i−3j+11k.
AAA, B B\,B and C C\,C are collinear, with AB:BC=1:2AB : BC = 1 : 2AB:BC=1:2.
Find the value of p p\,p and the value of qqq.
Find the exact length of ACACAC.
133 exam-style questions on WJEC A Level Maths 4.11 Vectors (A-level only), covering 4.11.1 Vectors (A-level only) and 4.11.2 Vectors (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.