1. The Cartesian system is also called as
a) Circular coordinate system
b) Rectangular coordinate system
c) Spherical coordinate system
d) Space coordinate system
Explanation: The other name for Cartesian is rectangular system, which is given by (x,y,z).
2. The volume of a parallelepiped in Cartesian is
a) dV = dx dy dz
b) dV = dx dy
c) dV = dy dz
d) dV = dx dz
Explanation: The volume of a parallelepiped is given by product of differential length, breadth and height.
3. A charge is placed in a square container. The position of the charge with respect to the origin can be found by
a) Spherical system
b) Circular system
c) Cartesian system
d) Space coordinate system
Explanation: Since the container possesses dimensions of a square (length, breadth and height), it can be found by Cartesian system
4. The scalar factor of Cartesian system is unity. State True/False.
a) True
b) False
Explanation: The range of Cartesian system is one to infinity. Thus the minimum scalar value of the system is unity.
5. The angular separation between the vectors A = 4i + 3j + 5k and B = i – 2j + 2k is (in degrees)
a) 65.8
b) 66.8
c) 67.8
d) 68.8
Explanation: The dot product the vector is 8. Angle of separation is cos θ = 8/ (7.07 X 3) = 0.377 and θ = cos-1(0.377) = 67.8.
6. The Cartesian coordinates can be related to cylindrical coordinates and spherical coordinates. State True/False.
a) True
b) False
Explanation: All the coordinate systems are inter-convertible and all the vector operations are applicable to it.
7. Transform the vector A = 3i – 2j – 4k at P(2,3,3) to cylindrical coordinates
a) -3.6j – 4k
b) -3.6j + 4k
c) 3.6j – 4k
d) 3.6j + 4k
Explanation: Convert the Cartesian form to cylindrical form by formula and substitute the points to get -3.6j – 4k
8. The spherical equivalent of the vector B = yi + (x + z)j located at (-2,6,3) is given by
a) (7,64.62,71.57)
b) (7,-64.62,-71.57)
c) (7,-64.62,71.57)
d) (7,64.62,-71.57)
Explanation: Substitute the points in the vector and convert the Cartesian to cylindrical form to get radius as 7, plane angle1 as 64.62 and plane angle2 as -71.57.
9. Which of the following criteria is used to choose a coordinate system?
a) Distance
b) Intensity
c) Magnitude
d) Geometry
Explanation: The coordinate system is chosen based on the geometry of the given problem. From a point charge +Q, the electric field spreads in all 360 degrees. The calculation of electric field in this case will be spherical system.
10. Vector transformation followed by coordinate point substitution and vice-versa, both given the same result. Choose the best answer.
a) Possible, when the vector is constant
b) Possible, when the vector is variable
c) Possible in all cases
d) Not possible
Explanation: The order of vector transformation and point substitution will not affect the result, only when the vector is a constant.