JEE Advanced Mathematics: Vector Algebra Practice Questions

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

  1. Q1.
    Find the cross product of i and j.
    Easy
  2. Q2.
    If a vector has direction cosines 1/sqrt(3), 1/sqrt(3), and 1/sqrt(3), what is its magnitude?
    Easy
  3. Q3.
    If the vectors 2i - j + k and i + 2j - 3k are perpendicular, find the value of the dot product.
    Easy
  4. Q4.
    What is the projection of the vector i + j on the vector i - j?
    Easy
  5. Q5.
    Let a, b, and c be three unit vectors such that a dot b = 0 and a dot c = 0. If the angle between band c is 30 degrees, then find the value of |across (b cross
    Medium
  6. Q6.
    Let a, b, and c be three unit vectors such that across (b cross c) = (1/2)b. If the angle between band c is theta, then the value of sin squared theta is equal
    Hard
  7. Q7.
    Let a, b, and c be vectors such that |a| = 3, |b| = 4, and |c| = 5. If a + b + c = 0, then the value of a dot b + b dot c + c dot a is:
    Hard
  8. Q8.
    Let u, v, and w be vectors such that |u| = 1, |v| = 2, and |w| = 3. If the projection of v along u is equal to the projection of w along u, and v is perpendicul
    Hard
  9. Q9.
    If the vectors a = i + j + k, b = i - j + 2k, and c = xi + (x-2)j + k are coplanar, then the value of x is:
    Hard

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