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Vectors practice

QCE Specialist Maths · Original practice questions with worked solutions

All vectors practice questions

56 original questions · Page 3 of 3

  1. Q249 · Original practice · 12 marks
    A flexible cable runs from A=(1,1,4)A=(1,1,4) to B=(5,−1,2)B=(5,-1,2) through a junction PP on the floor z=0z=0. Coordinates are in metres. Its length is ∣AP∣+∣PB∣|AP|+|PB|. The junction is first free to move anywhere on the floor, then is constrained to the rail x+y=2x+y=2, z=0z=0.
    Vectors in two and three dimensions
  2. Q254 · Original practice · 12 marks
    A river is 100 m wide. Coordinates have xx east and yy north, with the near bank y=0y=0 and far bank y=100y=100. A rescue boat starts at (0,0)(0,0) and keeps a fixed velocity (ux,uy)(u_x,u_y) relative to the water, with ux2+uy2=25u_x^2+u_y^2=25 and uy>0u_y>0. The current at northward coordinate yy is 0.12y0.12y m/s east. A raft moves east along the far bank from (60,100)(60,100) at…
    Vector calculus
  3. Q268 · Original practice · 5 marks
    A nondegenerate parallelogram ABCD in three-dimensional space has position vectors a,b,c,d\mathbf a,\mathbf b,\mathbf c,\mathbf d in cyclic order. Let M and N be the midpoints of AB and DC.
    Vectors in two and three dimensions
  4. Q269 · Original practice · 5 marks
    Let A, B and C be noncollinear points with position vectors a,b,c\mathbf a,\mathbf b,\mathbf c. M is the midpoint of BC. Define G by g=(a+b+c)/3\mathbf g=(\mathbf a+\mathbf b+\mathbf c)/3.
    Vectors in two and three dimensions
  5. Q273 · Original practice · 7 marks
    A particle moves with r(t)=(1+2sec⁡t)i+(2+tan⁡t)j\mathbf r(t)=(1+2\sec t)\mathbf i+(2+\tan t)\mathbf j, for 0≤t<π/20\le t<\pi/2. Blank coordinate axes are supplied.
    Vector calculus
  6. Q288 · Original practice · 1 mark
    A position vector is a=3i+4j+5k\mathbf a=3\mathbf i+4\mathbf j+5\mathbf k. Its altitude angle above the xy-plane is
    Vectors in two and three dimensions
  7. Q289 · Original practice · 1 mark
    Let a=(2,−3,1)\mathbf a=(2,-3,1) and b=(−1,0,0)\mathbf b=(-1,0,0). The scalar projection of a onto b is
    Vectors in two and three dimensions
  8. Q297 · Original practice · 6 marks
    A particle has r(t)=4cos⁡(2t)i+4sin⁡(2t)j\mathbf r(t)=4\cos(2t)\mathbf i+4\sin(2t)\mathbf j metres. The question diagram shows its circular path and the point at t=π/8t=\pi/8 s.
    Vector calculus