JEE Main Mathematics: Vector Algebra Practice Questions

11 questions with answers and step-by-step solutions. Tap any question to see the full worked solution.

  1. Q1.
    Find the magnitude of the vector a = 3i + 4j - 12k.
    Easy
  2. Q2.
    If the magnitude of a vector a is 5, what is the magnitude of 3a?
    Easy
  3. Q3.
    If the vectors 2i + aj + k and 3i - 2j + 4k are perpendicular, find the value of a.
    Easy
  4. Q4.
    What is the projection of vector i + j on vector i - j?
    Easy
  5. Q5.
    If a = 2i + 2j + k and b = 6i - 3j + 2k, then the projection of a on b is
    Medium
  6. Q6.
    Let a and b be two unit vectors such that the angle between them is 60 degrees. Then the value of |a - b| is
    Medium
  7. Q7.
    The area of a triangle whose adjacent sides are represented by the vectors a = 3i + j + 2k and b = i - j + k is
    Medium
  8. Q8.
    If the vectors 3i + j - k and 2i - j + mk are perpendicular, then the value of m is
    Medium
  9. Q9.
    Let a and b be two vectors such that |a| = 1, |b| = 4, and a dot b = 2. If c = (2a x b) - 3b, then find the angle between a and c.
    Hard
  10. Q10.
    If the vectors a = i + j + k, b = i - j + 2k, and c = x i + (x - 2) j - k are coplanar, then find the value of x.
    Hard
  11. Q11.
    Let a, b, and c be three unit vectors such that a + b + c = 0. If the vector d = a x b + b x c + c x a, then what is the magnitude of d?
    Hard

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Vector Algebra — JEE Main Mathematics Practice Questions with Solutions | SolveGini