Class XII Maths 3D Geometry 4

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Question 1

Direction ratios of two lines are a, b, c and , , . The lines are -

• AMutually perpendicular
• BParallel
• CCoincident
• DNone of these

Question 2

If l, m, n and l′, m′, n′be the direction cosines of two lines which include an angle θ, then -

• Acosθ= ll′+ mm′ + nn′
• Bsinθ= ll′+ mm′ + nn′
• Ccosθ= mm′ + m′n + nl′+n′l+ lm′+ l′m
• Dsinθ= mn′ + m′n + nl′+ n′l+ lm′+ l′m

Question 3

The line joining origin to the points of intersection curves ax² + 2hxy + by² + 2gx = 0 and a₁x² + 2h₁xy + b₁y² + 2g₁x = 0 will be mutually perpendicular if

• Ag(a₁ + b₁) = g₁(a + b)
• Bg(a + b) = g₁(a₁ + b₁)
• Ca + b = gg₁(a₁ + b₁)
• Dag + a₁g₁ = bg + b₁g₁

Question 4

Let be a fixed angle. If and then Q is obtained from P by

• Aclockwise rotation around the origin through an angle α
• Banticlockwise rotation around the origin through an angle α
• Creflection in the line through origin with slope tanα
• Dreflection in the line through the origin with slope tan(α/2)

Question 5

If the angle θ between the line and the plane 2x - y + z + 4 = 0 is such that sin θ = 1/3 the value of λ is

• A
• B
• C
• D

Question 6

The angle between the lines 2x = 3y = - z and 6x = - y = - 4z is

• A0⁰
• B90⁰
• C45⁰
• D30⁰

Question 7

The intersection of the spheres and is the same as the intersection of one of the sphere and the plane

• Ax – y – z = 1
• Bx – 2y – z = 1
• Cx – y – 2z = 1
• D2x – y – z = 1

Question 8

A point P(x, y, z) moves parallel to z-axis. Which of the three variable x, y, z remain fixed?

• Ax and y
• By and z
• Cx and z
• Dnone of these

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