NATIONAL OPEN UNIVERSITY OF NIGERIA
Plot 91, Cadastral Zone, Nnamdi Azikiwe Expressway, Jabi, Abuja.
FACULTY OF SCIENCES
DEPARTMENT OF MATHEMATICS
JULY EXAMINATION 2017_1
Course Code: MTH303
Course Title: VECTORS AND TENSORS
Credit Unit: 3
Time Allowed: 3 HOURS
Total Marks: 70%
Instruction: ATTEMPT QUESTIONS NUMBER ONE (1) AND ANY OTHER FOUR (4) QUESTIONS
1. (a) Given a vector and
Find (i) and (ii) x at the point (1,-1,1) (6 Marks)
(b) Find the directional derivatives of at the point (1,1,-1) in the direction toward the point (-3,5,6). (6 Marks)
(c) Find the values of the constants a, b, c so that the directional derivative of at (1,2,-1) has a maximum of magnitude 64 in a direction parallel to the z-axis. (5 Marks)
(d) Evaluate divergence of at the point (1,1,1) . (5 Marks)
2. (a) Determine the constant b such that is solenoidal. (4 Marks)
(b) If f and g are solutions of the Laplace equation show that (4 Marks)
(c) Find the curl of at the point (1,2,3) (4 Marks)
3. (a) Given that , find a scalar function f(x, y, z) such
that . (3 Marks)
(b) Find the work done in moving a particle in the force field along
(i) Straight line from (0,0,0) to B(2,1,3) (3 Marks)
(ii) Space curve y=t, from t=0 to t =1 (3 Marks)
(iii) Curve c: defined by , from x=0, x = 2. (3 Marks)
4. (a) If evaluate around the curve c consisting of
and (4 Marks)
(b) Evaluate (i) x F) . ndS and (4 Marks)
(ii) if and S is the surface of the plane bounded by the coordinate planes x=0, y=0 and z=0 (4 Marks)
5. (a) Find the surface area of the plane cut of by x =0, y=0 and
(4 Marks)
(b) (i) If V is the region in the first octant bounded by and the plane x = 2 and . Evaluate (4 Marks)
(ii) Find the volume enclosed between two surfaces and
(4 Marks)
6. (a) Using Green’s theorem, find the area of the region in the first quadrant bounded by the
curves y = x, y = 1/x, y = x/4 (4 Marks)
(b) (i) Show that is a vector perpendicular to the surface where c is a constant
(4 Marks)
(ii) Find a unit normal to the surface at the point (2,-2,3) (4 Marks)
You can get the exam summary answers for this course from 08039407882
Check anoda sample below
