Get premium membership and access revision papers, questions with answers as well as video lessons.

Got a question or eager to learn? Discover limitless learning on WhatsApp now - Start Now!

Sma 2220: Vector Analysis Question Paper

Sma 2220: Vector Analysis

Course:Bachelor Of Science In Computer Science

Institution: Dedan Kimathi University Of Technology question papers

Exam Year:2013

DEDAN KIMATHI UNIVERSITY OF TECHNOLOGY
SECOND YEAR FIRST SEMESTER EXAMINATION
FOR THE DEGREE OF BACHELOR OF SCIENCE IN COMPUTER SCIENCE
SMA 2220: VECTOR ANALYSIS
DATE: 2013 TIME: 2 HOURS
INSTRUCTIONS Answer Question One and any other Two Questions
QUESTION ONE (30 MARKS)
a) A particle moves along the space curve ? ? 3 2 2 3 2sin5 t r t t i e j t k ? ? ? ? ? find the
magnitude of
a) velocity
b) Acceleration at any time t (5 marks)
b) If
A ? x2 cos yi ? z2 sin y j ? x2 y k find dA (4 marks)
c) Find the directional derivative of 2 2 ? ? x yz ? 4xz at (1, -2, -1) in the direction 2iˆ ? ˆj ? 2kˆ
(8 marks)
d) Given ? ? Fˆ ? xyiˆ ? x2 ? y2 ˆj find the value of
C
? F ?dr where C consists of the arc from
(2, 0) to (4, 2) (8 marks)
e) If A is a constant vector, prove that ??r ? Aˆ ? ? A (5 marks)
QUESTION TWO (20 MARKS)
a)Verify Green’s theorem in the plane for ? ? ? ? 2 2
C
? xy ? y dx ? x dy where C is the closed curve of
the region bounded by 2 y ? x and y ? x (9 marks)
b) If 1 A and 2 A are constant vectors and ? is a constant scalar , show that
? ? 1 2 sin cos x H e A y i A y j ? ? ? ? ? ? satisfies the partial differential equation
2 2
2 2
ˆ ˆ
0
d H d H
dx dy
? ?
(6 marks)
a) find the volume of a pallelopiped with sides
A ? 3i ? j B ? j ? 2k C ? i ?5 j ? k (5 marks)
QUESTION THREE (20 MARKS)
a) Given the space curve x ? acost y ? asint z ? bt
show that
2 2 2 2 ) )
a b
a b
a b a b
? ? ? ?
? ?
(8 marks)
b)
2 2 2 2 R ? x y i ? 2y z j ? xy z k Find
2 2
2 2
R R
x y
? ?
?
? ?
at the point (2, 1, -2)
(6 marks)
c) Determine whether ? ? 3 2 F ? y i ? 3xy ? 4 j is conservative in the entire plane and if it is
find its potential function (6 marks)
QUESTION FOUR (20 MARKS)
a) Given that Aˆ ? 2iˆ ?t 2 ˆj , ˆ sin3 ˆ ˆ ˆ t B ? t i ?t j ?e k and Cˆ ? ?3iˆ ?5 ˆj ? 2kˆ Differentiate with
respect to t
i. Cˆ ? Aˆ
ii. Cˆ ?Bˆ
iii. Cˆ ??Aˆ ?Bˆ ? (11 marks)
b) Given 2 F ? 2xz i ? x j ? y k evaluate ??? F dV where V is the region bounded by the surface
2 x ? 0, y ? 0, y ? 6, z ? x , z ? 4 (9 marks)
QUESTION FIVE (20 MARKS)
a)
Evaluate
S
?? F ?nds , where 2 F ? 2xyi ? yz j ? xz k and S is the surface of the region
bounded by x ? 0, y ? 0, y ? 3, z ? 0, x ? 2z ? 6
(6 marks)
b) Evaluate ? ? ? ? 2 ? 3x ? 2y dx ? x ?3cos y dy around the parallelogram having vertices (0, 0) , (2, 0)
, (3, 1) and (1, 1) (7marks)
c) if ? ? Pˆ ? xiˆ ? x2 ˆj ? x ?1 kˆ and Q ? 2x2 iˆ ? 6x kˆ evaluate
i)
2
0
ˆ ˆP
? ?Q dx ii)
2
0
ˆ ˆP
? ?Q dx (7 marks)

Sma 2220: Vector Analysis Question Paper

More Question Papers

Popular Exams