1
ASSIGNMENT No. 2
(Units 1–9) Total Marks: 100
Q.1 a) A comet has a parabolic orbit with the sun at the focus. The shortest distance
of the comet from the sun is 25,000,000 km. When the comet is 100 million
km form the sun, what is the angle of the line joining sun and the comet?
b) If the difference of any point P(x,y) on the hyperbola from (3,3) and (8,2) is
5, then find the equation of the hyperbola.
Q.2 a) Find the equations of the tangent and normal to the ellipse
22
1
49
xy
at (2, 3).
b) Discuss the conic
22
5 72 11 16 0x xy y
and find its elements.
Q.3 a) If
2 3 4 , 3 6 2a i j k b i j k and w i j k
. Find a unit vector
parallel to 3a - 2b + 4c.
b) Find the area pf the parallelogram with adjacent vectors
2 4 2u i j k and v i j k
Q.4 a) A force of magnitude 10 units acting, parallel to the vector
4 3 5i j k
,
displaces the point of application from (2, 3, 4) to (6, 4, 8). Find the work
done by that force.
b) Find the volume of the parallelepiped determined by
3 5 , 4 3 2 2 5a i j k b i j k and c i j k
Q.5 a) Solve the differential equation
3
31
x
dy e
dx y
b) Determine the value of
such that the lines 4x-3y-8=0
3 6 0, 2 0x y x y
are concurrent. Also find the point where they
meet.
docsity.com
