Question

Which of the following statements is/are correct

1. The magnitude of the vector 3 i + 4 j is 5 
2. A force (3 i + 4 j) N acting on a particle cause a displacement 6 j. The work done by the force is 30 N 
3. If vector (A and B) represent two adjacent sides of a parallelogram, then vector (A x B) give the area of that parallelogram.  
4. A force has magnitude 20 N. Its component in a direction making an angle 60° with the force is 10√3 N. 

Answer 1

Correct Answer : 1. The magnitude of the vector 3 i + 4 j is 5

Explanation :

a) Magnitude of 3 i + 4 j = 9 + 16 = 5

b) Work done = ∫ vector (F . ds) = vector (F . Δs) = (3 i + 4 j) .  6 j = 24 N

c) conceptual 

d) Component of vector in direction making angle with the vector 

= A cos θ 

= 20 cos 60° = 20 x 1/2

= 10 N