Class XII Maths 3D Geometry 1

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Question 1

The equation of the line passing through (2, 3, -1) and lying in the plane 2x + y – 5z – 12 = 0 and perpendicular to the line 2x + y – 5z – 12 = 0 = 4x – 3y + 7z is

• A
• B
• C
• D

Question 2

The image of the line in the plane 2x – y + z + 3 = 0 is the line

• A
• B
• C
• D

Question 3

The projections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector are

• A6, –3, 2
• B
• C
• D

Question 4

A line makes the same angle θ, with each of the x and z axis. If the angle β, which it makes with y-axis, is such that, then equals

• A
• B
• C
• D

Question 5

A line with direction cosines proportional to 2, 1, 2 meets each of the lines x = y + a = z and
x + a = 2y = 2z. The co-ordinates of each of the point of intersection are given by

• A(3a, 3a, 3a), (a, a, a)
• B(3a, 2a, 3a), (a, a, a)
• C(3a, 2a, 3a), (a, a, 2a)
• D(2a, 3a, 3a), (2a, a, a)

Question 6

If a line makes an angle of π/4 with the positive directions of each of x–axis and y–axis, then the angle that the line makes with the positive direction of the z–axis is

• Aπ/4
• Bπ/2
• Cπ/6
• Dπ/3

Question 7

If (2, 3, 5) is one end of a diameter of the sphere x² + y² + z² – 6x – 12y – 2z + 20 = 0, then the coordinates of the other end of the diameter are

• A(4, 3, 5)
• B(4, 3, –3)
• C(4, 9, –3)
• D(4, –3, 3)

Question 8

The angle between two lines and is-

• Acos^–1 (2/9)
• Bcos^–1 (4/9)
• Ccos^–1 (5/9)
• Dcos^–1 (7/9)

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