Answer only one of the following two alternatives. EITHER The lines l₁ and l₂ have equations r = 6i – 3j + s(3i – 4j – 2k) and r = 2i – j – 4k + t(i – 3j – k) respectively. The point P on l₁ and the point Q on l₂ are such that PQ is perpendicular to both l₁ and l₂. Show that the position vector of P is 3i + j + 2k and find the position vector of Q. Find, in the form r = a + λb + µc, an equation of the plane Π which passes through P and is perpendicular to l₁. The plane Π meets the plane r = pi + qj in the line l₃. Find a vector equation of l₃.

The plane Π₁ has equation r = [[2], [3], [-2]] + s[[1], [0], [-1]] + t[[0], [-1], [-2]]. Find a cartesian equation of...

The line l₁ is parallel to the vector i – 2j – 3k and passes through the point A, whose position vector is 3i + 3j - ...

Answer only one of the following two alternatives. EITHER The points A, B and C have position vectors i, 2j and 4k r...

It is given that e is an eigenvector of the matrix A, with corresponding eigenvalue λ.

The curves C₁ and C₂ have equations y = ax/(x+5) and y = (x² + (a + 10)x + 5a + 26)/(x+5) respectively, where a is a ...

Answer only one of the following two alternatives. EITHER The curve C₁ has polar equation r² = 2θ, for 0 ≤ θ < ½π.