cameroon gce A level June 2010 further mathematics 2
cameroon gce A level June 2010 further mathematics 2
2. The position vectors of the points π¨, π©, πͺ, π« with respect to the origin πΆ are π, π, π, π
respectively, where
π = 7π + 2π + π, π = π – 3π + 5π, π = π + π – 4π, π
= 2π – π + 3π.
Find:
a. The Cartesian equation of the plane π¨π©πͺ.
b. The Cartesian equation of the plane π©πͺπ«.
c. The cosine of the acute angle between the planes π¨π©πͺ and π©πͺπ«.
d. The area of the triangle π©πͺπ«.
e. The volume of the tetrahedron π¨π©πͺπ«.
3. Prove that the equation of the normal to the rectangular hyperbola π₯π¦ = π2 at the point π (ππ‘, ππ‘) is π‘3π₯ – π‘π¦ =
π(π‘4 – 1).
The normal at π on the hyperbola meets the π₯ –axis at π and the tangent π meets the π¦ – axis π
. Show that
the locus of the midpoint of ππ
, as π varies is 2π2π₯π¦ + π¦4 = π4.
4.
a. Find the root mean square value of tanh π₯, for 0 β€ π₯ β€ 2.
b. A curve is given parametrically by π₯ = cosh2 π‘ , π¦ = sinh2 π‘ , 0 β€ π‘ β€ 2.
