MCQ on Three Dimensional Geometry: To be an expert in JEE Mathematics, it is absolutely necessary to practice and be familiar will all the concepts as well as the questions of different types. This is essential to gain mastery over the subject. We have also often heard the common saying, “Practice Makes a Man Perfect”, hence students have to practice, practice and practice till they master the subject.

In this post we are providing you MCQ on Three Dimensional Geometry, which will be beneficial for you in upcoming JEE and Engineering Exams.

MCQ on Three Dimensional Geometry

Q1.  The direction ratios of the normal to the plane 7x + 4y – 2z + 5 = 0 are _______.
a)  7, 4,-2
b) 7, 4, 5
c) 7, 4, 2
d) 4, -2, 5

Q2. If a line has direction ratios 2, – 1, – 2, determine its direction cosines _______.
a) ⅓, ⅔, -⅓
b) ⅔, -⅓, -⅔
c) -⅔, ⅓, ⅔
d) None of the above

Q3. If the lines x-2/1 =y-2/1 =z-4/k and x-1/k = y-4/2 = z-5/1 are coplanar, then k can have _______.
a) Exactly two values
b) Exactly three values
c) Exactly one value
d) Any value

Q4.  The direction cosines of the y-axis are ______.
a) (9, 0, 0)
b) (1, 0, 0)
c) (0, 1, 0)
d) (0, 0, 1)

Q5. What are the direction cosines of the equation of the plane 2x + 3y – z = 5?
a) 1/√14, 3/√14, -2/√14
b) 2/√14, 3/√14, -1/√14
c) 2/√14, 1/√14, -1/√14
d) 2/√14, -2/√14, -3/√14

Q6. The vector equation for the line passing through the points (–1, 0, 2) and (3, 4, 6) is
a) i + 2k + λ(4i + 4j + 4k)
b) i – 2k + λ(4i + 4j + 4k)
c) -i + 2k+ λ(4i + 4j + 4k)
d) -i + 2k+ λ(4i – 4j – 4k)

Q7. Find the equation of the plane passing through the points P(1, 1, 1), Q(3, -1, 2), R(-3, 5, -4).
a) x + 2y = 0
b) x – y – 2 = 0
c) -x + 2y – 2 = 0
d) x + y – 2 = 0

Q8. Direction ratio of line joining (2, 3, 4) and (−1, −2, 1), are _____.
a) (−3, −5, −3)
b) (−3, 1, −3)
c) (−1, −5, −3)
d) (−3, −5, 5)

Q9. If l, m, n are the direction cosines of a line, then _____.
a) l²+ m²+ 2n² = 1
b) l²+ 2m²+ n² = 1
c) 2l²+ m²+ n² = 1
d) l²+ m²+ n² = 1

Q10. The equation x² – x – 2 = 0 in three-dimensional space is represented by _______.
a) A pair of parallel planes
b) A pair of straight lines
c) A pair of the perpendicular plane
d) None of these

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By Team Learning Mantras