CBSE Class 12 Mathematics 3D Geometry Worksheet Set A

Read and download free pdf of CBSE Class 12 Mathematics 3D Geometry Worksheet Set A. Download printable Mathematics Class 12 Worksheets in pdf format, CBSE Class 12 Mathematics Chapter 11 Three Dimensional Geometry Worksheet has been prepared as per the latest syllabus and exam pattern issued by CBSE, NCERT and KVS. Also download free pdf Mathematics Class 12 Assignments and practice them daily to get better marks in tests and exams for Class 12. Free chapter wise worksheets with answers have been designed by Class 12 teachers as per latest examination pattern

Chapter 11 Three Dimensional Geometry Mathematics Worksheet for Class 12

Class 12 Mathematics students should refer to the following printable worksheet in Pdf in Class 12. This test paper with questions and solutions for Class 12 Mathematics will be very useful for tests and exams and help you to score better marks

Class 12 Mathematics Chapter 11 Three Dimensional Geometry Worksheet Pdf

Question. The vertices B and C of a “ABC lie on the line, x + 2 / 3 = y - 1 / 0 = z/4 such that BC = 5 units. Then the area (in sq. units) of this triangle, given that the point A (1, –1, 2), is:
(a) 5√17
(b) 2√34
(c) 6
(d) √34
Answer : C

Question. The length of the pro ection of the line segment oining the points (5, –1, 4) and (4, –1, 3) on the plane, x + y + = 7 is:
(a) 2/3
(b) 1/3
(c) √2/3
(d) 2/√3
Answer : C

 

Question. A line AB in three-dimensional space makes angles 45and 120 with the positive x-axis and the positive y-axis respectively. If AB makes an acute angle q with the positive-axis, then q equals
(a) 45o
(b) 60o
(c) 75o
(d) 30o
Answer : B

Question. A line in the 3-dimensional space makes an angle θ (0 < 0 ≤ π/2) with both the x and y axes. Then the set of all values of θ is the interval: 
(a) (0, π/4]
(b) [π/6, π/3]
(c) [π/4, π/2]
(d) [π/3, π/2]
Answer : C

Question. The angle between the lines whose direction cosines satisfy the equations l + m+ n = 0 and l2 + m2 + n2 is
(a) π/6
(b) π/2
(c) π/3
(d) π/4
Answer : C

Question. A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(–1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is:
(a) cos-1(17/31)
(b) cos-1(19/31)
(c) cos-1(9/31)
(d) cos-1(7/31)
Answer : B

Question. If the pro ections of a line segment on the x, y and z-axes in 3-dimensional space are 2, 3 and 6 respectively, then the length of the line segment is :
(a) 12
(b) 7
(c) 9
(d) 6
Answer : B

Question. A plane P meets the coordinate axes at A, B and C respectively.
The centroid of ΔABC is given to be (1,1,2). Then the equation of the line through this centroid and perpendicular to the plane P is: 
(a) x - 1 /2 = y - 1 / 1 = z - 2 / 1
(b) x - 1 /1 = y - 1 / 1 = z - 2 / 2
(c) x - 1 /2 = y - 1 / 2 = z - 2 / 1
(d) x - 1 /1 = y - 1 / 2 = z - 2 / 2
Answer : C

Question. If (a, b, c) is the image of the point (1, 2, –3) in the line, x +1 / 2 =  y - 3 / -2  = z/-1, then a + b + c is equals to:
(a) 2
(b) – 1
(c) 3
(d) 1
Answer : A

Question. ABC is triangle in a plane with vertices A (2, 3, 5), B (–1, 3, 2) and C (λ, 5, μ). If the median through A is equally inclined to the coordinate axes, then the value of (λ3 + μ3 + 5) is :
(a) 1130
(b) 1348
(c) 1077
(d) 676
Answer : B

Question. Let ABC be a triangle with vertices at points A (2, 3, 5), B (–1, 3, 2) and C (λ, 5, μ) in three dimensional space. If the median through A is equally inclined with the axes, then 
(λ, μ) is equal to :
(a) (10, 7)
(b) (7, 5)
(c) (7, 10)
(d) (5, 7)
Answer : C

Question. A line makes the same angle q, with each of the x and z axis. If the angle b, which it makes with y-axis, is such that sin2 β = 3sin2 θ then cos2 θ equals 
(a) 5/2
(b) 5/1
(c) 5/3
(d) 3/2
Answer : C

Question. The shortest distance between the lines x - 3/3 = y - 8/-1 = z - 3/1 and x + 3/-3 = y - 7/2 = z - 6/4 is
(a) 2√30
(b) 7/30√2
(c) 3√30
(d) 3
Answer : A

 

Question. The pro ections of a vector on the three coordinate axis are 6, –3, 2 respectively. The direction cosines of the vector are :
(a) 6/5. -3/5. 2/5
(b) 6/7. -3/7. 2/7
(c) -6/7. -3/7. 2/7
(d) 6, – 3, 2
Answer : B

 

Question. Two lines x - 3/1 = y + 1/3 = z - 6/-1 and x + 5/7 = y - 2/-6 = z - 3/4 intersect at the point R. The reflection of R in the xy- plane has coordinates :
(a) (2, –4, –7)
(b) (2, 4, 7)
(c) (2, –4, 7)
(d) (–2, 4, 7)
Answer : A

 

Question. Let A (2, 3, 5), B (– 1, 3, 2) and C (λ, 5, μ) be the vertices of a ΔABC. If the median through A is equally inclined to the coordinate axes, then:
(a) 5λ – 8μ = 0
(b) 8λ – 5μ = 0
(c) 10λ – 7μ = 0
(d) 7λ – 10μ = 0
Answer : C

Question. If a point R(4, y, z) lies on the line segment oining the points P(2, –3, 4) and Q(8, 0, 10), then distance of R from the origin is :
(a) 2√14
(b) 2√21
(c) 6
(d) √53
Answer : A

Question. If the lines x = ay + b, z = cy + d and x = a' z + b', y = c' z + d' are perpendicular, then: 
(a) ab' + bc' + 1 = 0
(b) cc' + a + a' = 0
(c) bb' + cc' + 1 = 0
(d) aa' + c + c' = 0
Answer : D

Question. If a line makes an angle of p / 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
(a) π/4
(b) π/2
(c) π/6
(d) π/3
Answer : B

Question. A perpendicular is drawn from a point on the line x - 1/2 = y + 1/-1 = z/1 to the plane x + y + z = 3 such that the foot of the perpendicular Q also lies on the plane x – y + z = 3. 
Then the co-ordinates of Q are :
(a) (1, 0, 2)
(b) (2, 0, 1)
(c) (–1, 0, 4)
(d) (4, 0, –1)
Answer : B

 

Question. The acute angle between two lines such that the direction cosines l, m, n, of each of them satisfy the equations l + m + n = 0 and l2 + m2 – n2 = 0 is :
(a) 15
(b) 30
(c) 60
(d) 45
Answer : C

Question. An angle between the lines whose direction cosines are given by the equations, l + 3m + 5n = 0 and 5lm – 2mn + 6nl = 0, is
(a) cos-1(1/8)
(b) cos-1(1/6)
(c)  cos-1(1/3)
(d)  cos-1(1/4)
Answer : B

Question. The length of the perpendicular from the point (2, –1, 4) on the straight line x + 3/10 = y - 2/-7 = z/1 is:
(a) greater than 3 but less than 4
(b) less than 2
(c) greater than 2 but less than 3
(d) greater than 4
Answer : A

Question. If the angle between the lines x/2 = y/2 = z/1 and 5 - x /-2 = 7y - 14/ P = z -3 /4 is cos–1(2/3) then P is equal to
(a) - 7/4
(b) 2/7
(c) - 4/7
(d) 7/2
Answer : D

Question. If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through (a, 7, 1) is , then a is equal to _________. 
Answer : 4

CBSE Class 12 Mathematics 3D Geometry Worksheet Set A 1

CBSE Class 12 Mathematics 3D Geometry Worksheet Set A 2

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CBSE Class 12 Mathematics Chapter 11 Three Dimensional Geometry Worksheet

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