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.
- Q1.What is the projection of the vector i + j on the vector i - j?Easy
- Q2.Find the cross product of i and j.Easy
- Q3.If the vectors 2i - j + k and i + 2j - 3k are perpendicular, find the value of the dot product.Easy
- Q4.If a vector has direction cosines 1/sqrt(3), 1/sqrt(3), and 1/sqrt(3), what is its magnitude?Easy
- 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 crossMedium
- Q6.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
- 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
- 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 perpendiculHard
- Q9.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 equalHard
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