Class 11 Physics - Chapter Motion in a Plane NCERT Solutions | Establish the following vector inequalit
Establish the following vector inequalities geometrically or otherwise:
(a) |a + b| ≤ |a| + |b|
(b) |a + b| ≥ ||a| − |b||
(c) |a − b| ≤ |a| + |b|
(d) |a − b| ≥ ||a| − |b||
When does the equality sign above apply?
(a) Let two vectors 
and 
be represented by the adjacent sides of a parallelogram OMNP, as shown in the given figure.
Here, we can write:
(b) Let two vectors and be represented by the adjacent sides of a parallelogram OMNP, as shown in the given figure.
In a triangle, each side is smaller than the sum of the other two sides.
Therefore, in ΔOMN, we have:
(c) Let two vectors and be represented by the adjacent sides of a parallelogram PORS, as shown in the given figure.
In a triangle, each side is smaller than the sum of the other two sides. Therefore, in ΔOPS, we have:
OS < OP + PS
(d) Let two vectors and be represented by the adjacent sides of a parallelogram PORS, as shown in the given figure.
More Questions From Class 11 Physics - Chapter Motion in a Plane
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Rain is falling vertically with a speed of 30 m s–1. A woman rides a bicycle with a speed of 10 m s–1 in the north to south direction. What is the direction in which she should hold her umbrella?
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On an open ground, a motorist follows a track that turns to his left by an angle of 60° after every 500 m. Starting from a given turn, specify the displacement of the motorist at the third, sixth and eighth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.
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(b) each component of a vector is always a scalar
(c) the total path length is always equal to the magnitude of the displacement vector of a particle
(d) the average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time
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Given a + b + c + d = 0, which of the following statements are correct:
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(b) adding a scalar to a vector of the same dimensions,
(c) multiplying any vector by any scalar,
(d) multiplying any two scalars,
(e) adding any two vectors,
(f) adding a component of a vector to the same vector. - Q:-
Three girls skating on a circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in Fig. 4.20. What is the magnitude of the displacement vector for each? For which girl is this equal to the actual length of the path skated?
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An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km/h. Compare its centripetal acceleration with the acceleration due to gravity.
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