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State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:
(a) adding any two scalars, (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.
A passenger arriving in a new town wishes to go from the station to a hotel located 10 km away on a straight road from the station. A dishonest cabman takes him along a circuitous path 23 km long and reaches the hotel in 28 min. What is (a) the average speed of the taxi, (b) the magnitude of average velocity? Are the two equal?
Given a + b + c + d = 0, which of the following statements are correct:
(a) a, b, c, and d must each be a null vector,
(b) The magnitude of (a + c) equals the magnitude of (b+ d),
(c) The magnitude of a can never be greater than the sum of the magnitudes of b, c, and d,
(d) b + c must lie in the plane of a and d if a and d are not collinear, and in the line of a and d, if they are collinear?
Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.
Read each statement below carefully and state with reasons, if it is true or false:
Three vectors not lying in a plane can never add up to give a null vector.
Read each statement below carefully and state, with reasons and examples, if it is true or false:
A scalar quantity is one that
(a) is conserved in a process
(b) can never take negative values
(c) must be dimensionless
(d) does not vary from one point to another in space
(e) has the same value for observers with different orientations of axes
- Motion in plane part 12 (Position Vector and Displacement)
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- Motion in plane part 9 (Example Vectors)
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- Motion in plane part 10 (Example Vectors)
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- Motion in plane part 11 (Position Vector)
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- Motion in plane part 3 (Combination of Vector)
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- Motion in plane part 2 (Combination of Scalar)
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- Motion in plane part 8 (Example Vectors)
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- Physics Textbook for Class 11 Part 1