two questions i'm stuck on

Subject: two questions i'm stuck on Sat May 31, 2008 10:24 am

Super stuck on these two questions if anyone can help:

1.
S is a solid of revolution in 3-dimensions, formed by rotating a full turn about the
y-axis, the region in the ﬁrst quadrant of the (x, y)-plane bounded by the interval
[1, 2] on the y-axis, and the curve x = (2 − y)(y − 1)^2
(a) Find the volume, moment My and centre of mass of the solid object S .
(b) Formulate as an integral, but do not evaluate, the surface area of solid .

and:

2.
i. Find the magnitude of vector a = i + 2j + 2k.
ii. For b = 2i − j + 2k and c = 2i + 2j − k, show that b − c is perpendicular to a.
iii. Find the volume of the parallelepiped, with three concurrent edges formed by the
position vectors a, b and c.

thanks

Active member

2.

i)mag is: [(1)² +(2)² +(2)²]^1/2 = 3

ii) b-c=-3j+3k and (b-c).a=0 and hence perpendicular

iii)vol of a parallelopiped formed by 3 vectors = |a.(b*c)|
where a,b,c = vectors
* = cross product

can't answer 1 cos i haven't read that yet.......

by the way dude u should have posted this question in class xi th forum ..........

Active member

yah..you should have posted it in xi forum. i got a heart attack when i saw the question.