HOT PRACTICE TEST
Chapter 10 – Vector Algebra
Class XII Mathematics • 25 Marks
Vector Representation
Section A – 6 × 1 = 6
1. Find the magnitude of 3i+4j.
2. When are two vectors parallel?
3. What is the scalar product of perpendicular vectors?
4. State the magnitude of a unit vector.
5. What is a null vector?
6. Write the vector joining A(x₁,y₁,z₁) to B(x₂,y₂,z₂).
Section B – 3 × 2 = 6
1. Find the angle between i+j and i−j.
2. Find a unit vector in the direction of 2i−j+2k.
3. Determine whether 2i−j+k and 4i−2j+2k are parallel.
Section C – 3 × 3 = 9
1. Find the projection of 2i+3j+k on i−j.
2. Find the area of the parallelogram formed by a=i+j and b=2i−j.
3. Find λ if vectors (λ,2,3) and (2,4,6) are parallel.
Section D – 1 × 4 = 4
1. Using the vector product, derive the area of the triangle formed by three points with position vectors a,b,c. Explain why the magnitude of the cross product is relevant.