Class XII Maths 3D Geometry 6: Important Questions

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Question 1

The shortest distance between the lines = = and == is-

• A
• B2
• C5
• D3√30

Question 2

The points A(5, –1, 1); B(7, –4, 7); C(1, –6, 10) and D(–1, –3, 4) are vertices of a -

• Asquare
• Brhombus
• Crectangle
• Dnone of these

Question 3

Points (1, 2, 3); (3, 5, 7) and (–1, –1, –1) are-

• AVertices of a equilateral triangle
• BVertices of a right angle triangle
• CVertices of a isosceles triangle
• DCollinear

Question 4

A tetrahedron has vertices at O (0, 0, 0), A (1, 2, 1), B (2, 1, 3) and C (− 1, 1, 2). Then the angle between the faces OAB and ABC will be

• Acos⁻¹
• Bcos⁻¹
• C30⁰
• D90⁰

Question 5

If line = (–2–) + λ(2++2) is parallel to the plane . (3–2–m) = 14, then the value of m is

• A2
• B–2
• C0
• Dcannot be predicted with these information

Question 6

The angle of intersection of the normals at the point of the curves x² – y² = 8 and 9x² + 25y² = 225 is

• A0
• B
• C
• D

Question 7

If the lines and are at right angles, then the value of k will be –

• A
• B
• C–10
• D–7

Question 8

A plane meets the co-ordinate axes in A, B, C such that the centroid of the triangle is the point (1, r, r²), the equation of the plane is -

• Ax + ry + r²z = 3r²
• Br²x + ry + z = 3r²
• Cx + ry + r²z = 3
• Dr²x + ry + z = 3

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