Questions on Vector analysis

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Instructor: Saurabh verma

B.Tech, IIT Kanpur

mob: 09956551609

Q.1: What do you understand by scalar quantities and vector quantities? Explain with example.

Q.2: If two vectors A and B are acting at a point with angle q. Derive an equation for magnitude and direction of resultant R using Parallelogram method.

Q.3: Resultant of two vectors P and Q is R if we reverse the direction of Q then resultant becomes S. Prove

R² + S² = 2 (P² + Q²)

Q.4: If ABCDEF is a regular hexagon, prove the followings:

AB + AC + AD + AE + AF = 3 AD

Q.5: If | A X B | = Ö3 A – B, find out the value of A + B.

Q.6: If A = 3 i + 5 j, B = 2 i + 4 j ; Find out the followings:

1. Angle between A and B
2. A.B
3. A X B
4. (A + B). B

Q.7: If P X Q = R, state the true/false about the followings:

1. R is perpendicular to P
2. R is perpendicular to Q
3. R is perpendicular to (P + Q)
4. R is perpendicular to (P X Q)

Q.8: If two force of magnitude 6 N and 8 N acting on a point with angle 60^o. Find out the magnitude and direction of resultant.

Q.9: If magnitude of two perpendicular vectors P and Q is 5 and 7 respectively. Use vector diagram to show the P + Q and P – Q and find out the magnitude and direction.

Q.10: A car is moving on horizontal ground with velocity V m/s. The driver of car observes the rain to be falling vertically downwards with velocity 2V m/s. What is the velocity and direction of the rain?

Q.11: A man is swimming across a river at angle of 120^o. He took 100 seconds in crossing the river which is 10 m wide. Find out the followings:

1. Flow velocity of river
2. Speed of swimmer