Class 12 Maths MCQ – Three Dimensional Geometry – Angle between Two Planes – 2

This set of Class 12 Maths Chapter 11 Multiple Choice Questions & Answers (MCQs) focuses on “Three Dimensional Geometry – Angle between Two Planes – 2”.

1. _____ is the angle between the normals to two planes.
a) Normal between the planes
b) The angle between the planes
c) Tangent between the planes
d) Distance between the planes
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2. If θ is the angle between the planes a₁x + b₁y + c₁z + d₁ = 0 and a₂x + b₂y + c2₁z + d₂ = 0 then
cos θ=\(\frac {a1a2.b1b2.c1c2}{\sqrt {a1^2+b1^2+c1^2} \sqrt {a2^2+b2^2+c2^2 }}\).
a) True
b) False
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3. What is the formula to find the angle between the planes a₁x + b₁y + c₁z + d₁ = 0 and a₂x + b₂y + c₂z + d₂ = 0?
a) cos θ=\(\frac {a1a2+b1b2+c1c2}{\sqrt {a1^2+b1^2+c1^2} \sqrt {a2^2+b2^2+c^2 }}\)
b) sec θ=\(\frac {a1a2+b1b2+c1c2}{\sqrt {a1^2+b1^2+c1^2} \sqrt{a2^2+b2^2+c2^2 }}\)
c) cos θ=\(\frac {a1a2.b1b2.c1c2}{\sqrt {a1^2+b1^2+c1^2} \sqrt{a2^2+b2^2+c2^2 }}\)
d) cot θ=\(\frac {a1a2+b1b2+c1c2}{\sqrt {a1^2+b1^2+c1^2} \sqrt{a2^2+b2^2+c2^2 }}\)
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4. Which trigonometric function is used to find the angle between two planes?
a) Tangent
b) Cosecant
c) Secant
d) Sine
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5. Find s for the given planes 2x + 2y + sz + 2 = 0 and 3x + y + z – 2 = 0, if they are perpendicular to each other.
a) 21
b) – 7
c) 12
d) – 8
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6. What is the relation between the the planes a₁x + b₁y + c₁z + d₁ = 0 and a₂x + b₂y + c2₁z + d₂ = 0, if their normal are parallel to each other?
a) \(\frac {a1}{b1} = \frac{a2}{c1} = \frac{c2}{b2}\)
b) \(\frac {a1}{a2} = \frac{b1}{c2} = \frac{c1}{b2}\)
c) \(\frac {a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}\)
d) \(\frac {c1}{a2} = \frac{b1}{b2} = \frac{a1}{c2}\)
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7. What is the relation between the planes a₁x + b₁y + c₁z + d₁ = 0 and a₂x + b₂y + c2₁z + d₂ = 0, if their normal are perpendicular to each other?
a) a₁a₂ . b₁b₂ . c₁c₂ = 0
b) a₁a₂ + b₁b₂ + c₁c₂ = 0
c) a₁a₂ + b₁b₂ – c₁c₂ = 0
d) a₁a₂ + b₁b₂ – c₁c₂ = 0
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8. _____ planes have an angle 90 degrees between them.
a) Orthogonal
b) Tangential
c) Normal
d) Parallel
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9. The condition a₁a₂ + b₁b₂ + c₁c₂ = 0 is for the planes whose normals are _____ to each other.
a) integral
b) parallel
c) perpendicular
d) concentric
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10. The condition \(\frac {a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2}\) is for the planes whose normals are _____ to each other.
a) perpendicular
b) parallel
c) differential
d) tangential
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11. Find the angle between 2x + 3y – 2z + 4 = 0 and 4x + 3y + 2z + 2 = 0.
a) 38.2
b) 19.64
c) 89.21
d) 54.54
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12. Find the angle between x + 2y + 7z + 2 = 0 and 4x + 4y + z + 2 = 0.
a) 69.69
b) 84.32
c) 63.25
d) 83.25
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13. The planes 5x + y + 3z + 1 = 0 and x + y – kz + 6 = 0 are orthogonal, find k.
a) 4
b) 2
c) 6
d) 8
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14. Find the angle between the planes 5x + y + 3z + 1 = 0 and x + y – 2z + 6 = 0.
a) 30.82
b) 34.91
c) 11.23
d) 7.54
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15. Find k for the given planes x + 2y + kz + 2 = 0 and 3x + 4y – z + 2 = 0, if they are perpendicular to each other.
a) 21
b) 17
c) 12
d) 11
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Sanfoundry Global Education & Learning Series – Mathematics – Class 12.

To practice all chapters and topics of class 12 Mathematics, here is complete set of 1000+ Multiple Choice Questions and Answers.