CBSE Class 11 Physics Units Dimensions Vectors Solved Examples

Ex.1. If A = 4i – 3j and B = 6i + 8j, find the scalar magnitude and direction of A, B, A + B, A – B and B – A with respect to positive direction of x-axis.

Ex.2. If vectors A = 3i + j – 2k, B = –i + 3j + 4k and C = 4i –2j –6k can be represented by the sides of a triangle, find the two vectors which will give the third vector as a resultant.
Sol.: If any one of these two vectors are added, their resultant should be equal to the third vector as their resultant.
A + B = (3i + j – 2k) + (–i + 3j + 4k) = 2i + 4j + 2k ≠ C
A + C = (3i + j – 2k) + (4i –2j –6k) = (7i – j – 8k) ≠ B
B + C = (–i + 3j + 4k) + (4i –2j –6k) = (3i + j –2k) = A
∴ vectors B and C combine to give resultant A

Ex.3 Find the scalar product and angle between vectors A = 3i – 5j and B = 6i + 2j

Ex.4 A partical moves from the position 2i + 3j – 5k to position 12i + 15j + 8k in metre units and a uniform force 5i + 2j + 3k , Newton acts on it. Calculate the work done by this force.
Sol.: If F is force applied to displace a particle through distance S, work W is given by
W = F . S
S = r2 – r1 = (12i + 15j + 8k) – (2i + 3j – 5k) = 10i + 12j + 13k
W = (5i + 2j + 3k) . (10i + 12j + 13k) = 50 + 24 + 39 = 113 J

Ex.5 If a force F = 4i – 10j Newton is applied to the rim of a disc at a distance or r = –5i – 4j from its axis of rotation, find the torque applied.

Ex.6: A plane is flying with speed 700 km/h in north-eastern direction and wind is blowing at 100 km/h north to south. Find the resultant displacement of plane in 2hours.
Sol.: Let v1 be velocity of plane in north eastern direction & v2 be velocity of wind from north to south and
i and j be unit vectors in east and north direction.