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1. The straight line l passes through the points A and B with position vectors 7i - 3j +6k and 10i +3k respectively. The plane p has equation 3x - y +2z = 8. Show that l is parallel to p.
The point C is the foot of the perpendicular from A to p.
Find a vector equation for the line which passes through C and is parallel to l.
2. The parametric equations of a curve are x = asint , y = atcost, where a is a positive constant and 0 <t<π/2. Find dy/dx in terms of t, and hence show that the gradient of the curve is zero where t = cot t.
By sketching a suitable pair of graphs, show that the equation t = cot t is satisfied by just one value of t in the relevant range.
Determine with reasons whether this value of t is greater than or less than π/4.
Please help me asap. I'm stucked. This questions are from CIE Specimen Paper!
The point C is the foot of the perpendicular from A to p.
Find a vector equation for the line which passes through C and is parallel to l.
2. The parametric equations of a curve are x = asint , y = atcost, where a is a positive constant and 0 <t<π/2. Find dy/dx in terms of t, and hence show that the gradient of the curve is zero where t = cot t.
By sketching a suitable pair of graphs, show that the equation t = cot t is satisfied by just one value of t in the relevant range.
Determine with reasons whether this value of t is greater than or less than π/4.
Please help me asap. I'm stucked. This questions are from CIE Specimen Paper!