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Coordinate Axes in Three Dimensional Space

A situation m...

Question

A situation may be described by using different sets coordinate axes having different orientation. Which the following do not depended on the orientation of the axis?
(a) the value of a scalar
(b) component of a vector
(c) a vector
(d) the magnitude of a vector.

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Solution

(a) the value of a scalar
(c) a vector
(d) the magnitude of a vector

The value of a scalar, a vector and the magnitude of a vector do not depend on a given set of coordinate axes with different orientation. However, components of a vector depend on the orientation of the axes.

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Q. A situation may be described by using different sets of co-ordinate axes having different orientations. Which of the following do not depend on the orientation of the axes -
(a) The value of a scalar
(b) Component of a vector
(c) A vector
(d) The magnitude of a vector

Q. A situation may be described by using different sets of coordinate axes having different orientations. Magnitude of which of the following do not depend on the orientation of the axis ?

Q. Choose the correct statements.
a) The product of a scalar and a vector is a vector quantity.
b) Two vectors of different magnitude can be combined to give a zero resultant.
c) Three vectors of different magnitudes may be combined to give a zero resultant.
d) All the above are wrong statements.

Q. If are two collinear vectors, then which of the following are incorrect : A. , for some scalar λ B. C. the respective components of are proportional D. both the vectors have same direction, but different magnitudes

Use the following information to answer the next question.

Three statements about scalars and vectors:

I. Vectors having different units cannot be multiplied with each other.

II. Two vectors are considered to be equal if they are of equal magnitude and have the same direction.

III. The multiplication of a scalar with a vector can give a scalar quantity.

Among the given statements,

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