1. The distance vector is obtained in
a) Cartesian coordinate system
b) Spherical coordinate system
c) Circular coordinate system
d) Space coordinate system
Explanation: Vector formed by connecting two points in space is distance vector. Thus, it is obtained in space coordinate system.
2. The divergence of distance vector is
a) 0
b) 3
c) 2
d) 1
Explanation: The distance vector of any coordinates is generally, r = xi + yj + zk. The divergence of r is 1 + 1 + 1 = 3.
3. Find a vector normal to a plane consisting of points p1(0,1,0), p2(1,0,1) and p3(0,0,1)
a) –j – k
b) –i – j
c) –i – k
d) –i – j – k
Explanation: Distance vector from p1 and p2 is a = i – j + k. Distance vector from p1 and p3 is b = –j + k. The vector normal to these points is a X b = -j – k.
4. The unit vector to the points p1(0,1,0), p2(1,0,1), p3(0,0,1) is
a) (-j – k)/1.414
b) (-i – k)/1.414
c) (-i – j)/1.414
d) (-i – j – k)/1.414
Explanation: The cross product of p1, p2, p3 is a X b = -j – k and its magnitude is 1.414. The unit normal vector is given by, (-j – k)/1.414.
5. The polar form of Cartesian coordinates is
a) Circular coordinates
b) Spherical coordinates
c) Cartesian coordinates
d) Space coordinates
Explanation: The radius in the polar coordinates is the Pythagorean triplet-(r,x,y).Thus it is the circular coordinates
6. The work-electric field relation is given by
a) Volume integral
b) Surface integral
c) Line integral
d) Relation impossible
Explanation: The work done is given by, W = -Q ∫E dl. Thus it is line integral
7. The distance vector can be used to compute which of the following?
a) Dot product
b) Cross product
c) Unit normal vector
d) Area
Explanation: The distance vector is the distance between two points on space, thus the unit normal vector is computed using the distance vector
8. Distance and position vectors rely on field strength. State True/False.
a) True
b) False
Explanation: Position or distance of a vector is dependent on the field strength
9. Find the projection of A on B. Given A = 10j + 3k and B = 4j + 5k.
a) 6
b) 6.25
c) 6.5
d) 6.75
Explanation: Projection of A on B = (A . B)/|B|. Thus the answer is 40/6.4= 6.25
10. The vector product of two vectors is given by area of the parallelogram. State True/False.
a) True
b) False
Explanation: The vector product of two vectors is A X B = AB sin θ. n, where n is the unit normal vector to the plane given by A and B. Their magnitude is given by |A X B|, which is the area of parallelogram.