### XI Physics | Dot Product Solved Numericals

Q.15 Find the angle between A=2i + 2j – k and B=6i – 3j +2k.
Q.16 Find the projection of the vector A= i – 2j + k on to the direction of vector B=4i – 4j +7k
Q. 17 Find the angles alpha, beta and gamma which the vector A=3i – 6j +2k makes with the positive x,y,z axis respectively.
Q.18 Find the work done in moving an object along a vector r=3i – 2j +5k is the applied force is F=2i – j – k.
Q.19 Find the work done by a force 30,000 N in moving an object through a distance of 45 m when :(a) force is in the direction of motion;(b) force makes an angle of 40 degrees to the direction of motion.Find the rate at which the force is working at a time when the velocity is 2 m/s.
Q.20 Two vectors A and B such that |A|=3, |B|=4 and A. B=-5 , find
(a) The angle between A and B.
(b) The Length |A+B| and |A-B|
(c) The angle between (A+B) and (A-B)