QCEVault

Vector calculus — Question 64

Original QCE Vault practice · 6 marks

Q64 · Practice questionComplex unfamiliar6 marks

QUESTION 64 (6 marks)

A sphere has centre C(2,−1,3)C(2,-1,3) and radius 5. It is cut by the plane 2x−y+2z=9.2x-y+2z=9. The intersection is a circle.
Supporting diagram for question 64
a)
Determine the centre of the circle of intersection.
[3 marks]
b)
Determine its exact radius.
[3 marks]
Question linkSyllabus coverage

Related questions

  1. Q9 · Original practice · 6 marks
    Original Specialist Mathematics practice question 9: motion in a plane
    Vector calculus
  2. Q32 · Original practice · 7 marks
    Two particles move for t≥0t\ge0 with positions rA(t)=(2t,t),rB(t)=(6−t,4−2t).\mathbf r_A(t)=(2t,t),\qquad\mathbf r_B(t)=(6-t,4-2t).
    Vector calculus
  3. Q34 · Original practice · 6 marks
    A particle follows the path r(t)=(3cos⁡t,2sin⁡t),0≤t≤2π.\mathbf r(t)=(3\cos t,2\sin t),\qquad0\le t\le2\pi.
    Vector calculus
  4. Q36 · Original practice · 6 marks
    A projectile is launched from level ground at 20 m s−120\ \mathrm{m\,s^{-1}} at 45∘45^\circ above the horizontal. Take g=10 m s−2g=10\ \mathrm{m\,s^{-2}} and ignore air resistance.
    Vector calculus