Worksheet: Angle between Two Planes

In this worksheet, we will practice finding the measure of an angle between two planes or that between a line and a plane.

Q1:

Find, to the nearest second, the measure of the angle between the planes 9𝑥6𝑦+5𝑧=8 and 2𝑥+2𝑦+7𝑧=8.

  • A483137
  • B651129
  • C864851
  • D75659

Q2:

Find, to the nearest second, the measure of the angle between the planes 5,9,4=6r and 4𝑥𝑦6𝑧=3.

  • A6354
  • B463721
  • C74959
  • D86266

Q3:

Find, to the nearest second, the measure of the angle between the straight line rijkijk=(9+85)+𝑡(+3) and the normal to the plane rijk(3+2+5)=7.

  • A512953
  • B128307
  • C263634
  • D38307

Q4:

Which of the following is the smaller angle between the straight line rijkijk=(79)+𝑡(2+) and the plane rijk(99+2)=13?

  • Asin74386
  • Bsin7249498
  • Ccos7249498
  • Dcos74386

Q5:

Find, to the nearest second, the measure of the smaller angle between the straight line 𝑥77=𝑦75=𝑧41 and the plane 6𝑥8𝑦5𝑧17=0.

  • A524045
  • B163253
  • C1271915
  • D371915

Q6:

If the angle between the two planes 𝑎𝑥4𝑦+5𝑧=5 and r(7,1,0)=4 is 60, find the value of the positive constant 𝑎.

Q7:

Find, to the nearest second, the measure of the angle between the straight line 𝑥=3𝑡1,𝑦=2𝑡+4,𝑧=5 and the plane 3𝑥4𝑦+𝑧=2.

  • A222248
  • B442512
  • C865255
  • D453448
  • E673712

Q8:

Find, to the nearest degree, the measure of the angle between the planes 2(𝑥1)+3(𝑦4)+4(𝑧+5)=0 and r(1,2,5)=16.

Q9:

Find, to the nearest degree, the measure of the angle between the planes 3𝑥2𝑦+3𝑧=7 and 2(𝑥1)+3(𝑦4)+4(𝑧+5)=0.

Q10:

If the angle between the plane 3𝑥+𝑏𝑦5𝑧=2 and the straight line 𝑥+2=3𝑦2=𝑧12 is 45, find the value of the positive constant 𝑏 given that 0<𝑏<10.

Q11:

Find, to the nearest degree, the measure of the angle between the plane 2(𝑥3)8(𝑦+2)+3𝑧=4 and the straight line𝑥36=𝑦+12=𝑧14.

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