IIT JEE Maths Practice Paper 14 – Vectors PYQs

IIT JEE Maths Practice Paper – Part 14: Vectors

Practice 10 multiple-choice questions from past JEE papers based on the topic of Vectors. Click submit to view your result, score, and explanations.

1. If vector a = 2i + 3j and vector b = i − j, then a · b is:
   1
   -1
   3
   5
2. If vectors a and b are such that |a| = 3, |b| = 4 and a · b = 6, then the angle between them is:
   30°
   45°
   60°
   90°
3. Two vectors are perpendicular if:
   Their magnitudes are equal
   Their dot product is zero
   Their cross product is zero
   They have opposite directions
4. The magnitude of the cross product of vectors a and b is equal to:
   ab cos θ
   ab
   ab sin θ
   a + b
5. The vector i + j is rotated 90° counterclockwise in the plane. Its new direction is:
   -j + i
   -i – j
   -i + j
   -j – i
6. If a vector has magnitude 5 and makes an angle of 60° with the x-axis, then its x-component is:
   5
   5√3
   5 cos 60°
   5 sin 60°
7. If a · b = 0 and a × b ≠ 0, then:
   Vectors are parallel
   Vectors are equal
   Vectors are perpendicular
   Vectors are same direction
8. Unit vector along vector 3i + 4j is:
   3i + 4j
   (3/5)i + (4/5)j
   (4/5)i + (3/5)j
   (5/3)i + (5/4)j
9. The projection of vector a on b is given by:
   |a||b| sin θ
   a · b / |b|
   a × b
   ab cos θ
10. If a = i + j and b = i − j, then a × b is:
    2k
    -2k
    0
    i + k

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