Lesson Worksheet: The Angle between Two Planes and between a Plane and a Straight Line Mathematics

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 r7,1,0=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 r1,2,5=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.

This lesson includes 16 additional questions and 171 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.