1. Write an example of zero vector.
2. State the essential condition for the addition of vectors.
3. When is the magnitude of (A + B) equal to the magnitude of (A − B)?
4. What is the maximum number of component into which a vector can be resolved?
5. Does a vector quantity depends upon frame of reference chosen ?
6. What is the unit vector perpendicular to the plane of vectors A and B ?
7. What is the angle between (A + B) and (A × B)?
8. Two vectors A & B are inclined to each other at an angle θ . Using Parallelogram law of vectors addition, find the magnitude and direction of their resultant.
9. When the angle between two vectors of equal magnitudes is 2π / 3, prove that the magnitude of the resultant is equal to either.
10. If A = 3ˆi + 4ˆj and B = 7ˆi + 24ˆj, find a vector having the same magnitude as B and parallel to A
11. (a) If ˆi and ˆj are unit vectors along x & y axis respectively then what is magnitude and direction of (ˆi + ˆj) and (ˆi − ˆj) ? (b) Find the components of vector a= 2ˆi + 3ˆj along the directors of vectors (ˆi + ˆj) and (ˆi − ˆj) .
12. A motorboat is racing towards north at 25 kmh–1 and the water current in that region is 10 kmh-1 in the direction of 60° east of south. Find the resultant velocity of the boat.
13. An aircraft is flying at a height of 3400 m above the ground. If the angle subtended at a
ground observation point by the aircraft position 10 second apart is 30°, what is the
speedof the aircraft?
14. A boat is moving with a velocity (3ˆi − 4ˆj) with respect to ground. The water in river is
flowing with a velocity (−3ˆi − 4ˆj) with respect to ground. What is the relative
velocity ofboat with respect to river?
15. If the magnitude of two vectors are 3 and 4 and their scalar product is 6, find angle between them.
16. Find the value of λ so that the vector A = 2ˆi + λˆj + Kˆ and B = 4ˆi − 2ˆj + 2Kˆ are perpendicular to each other.
17. (a) What is the sum in unit–vector notation of the two vectors a = 4.0i + 3.0j and b = −13.0i + 7.0j? (b) What are the magnitude and direction of a + b?
18. Vector a has magnitude 5.0 m and is directed east. Vector b has magnitude 4.0 m and is directed 35◦ west of north. What are (a) the magnitude and (b) the direction of a + b? What are (c) the magnitude and (d) the direction of b − a? Draw a vector diagram for each combination.
19. If a − b = 2c, a + b = 4c and c = 3i + 4j, then what are a and b?
Two equal forces are acting at a point with an angle of 60° between them. If the resultant force is equal to 20√3 N, find the magnitude of each force