Question

The diagram shows a semicircular prism with a horizontal rectangular base ABCD. The vertical ends AED and BFC are semicircles of radius 6 cm. The length of the prism is 20 cm. The mid-point of AD is the origin O, the mid-point of BC is M and the mid-point of DC is N. The points E and F are the highest points of the semicircular ends of the prism. The point P lies on EF such that EP = 8 cm.
Unit vectors i, j and k are parallel to OD, OM and OE respectively.
(i) Express each of the vector PN in terms of i, j and k.

Diagram Q4. http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20(9709)/9709_w08_qp_1.pdf

Answer 1

\( \bar {PA} = \bar {PE}+\bar {EO}+\bar {OA} \)
\( \bar {PA} = -\bar {EP}-\bar {OE}+\bar {OA} \)

Answer 2

PN ? I did PA already.

Answer 3

ok
drop a perpendicular to base from P
say X

PN = PX+XN

Answer 4

PX= EO
XN +OD

Answer 5

XN=OD ***

Answer 6

uh huh? so?

Answer 7

EO and OD are known, right ?

Answer 8

but the answer is 6i + 2j = 6k.

Answer 9

I got the answer as what you did. But it's wrong.

Answer 10

6i and -6k we are getting....wondering how they get 2j too...

Answer 11

ohhh! EP is 8, but DN is 10!

Answer 12

the top part EP is 8 whereas DN is 10.

Answer 13

Yeah.

Answer 14

right, we need to go 2 units in j direction too, thats where 2j comes from

Answer 15

But how? You cant simply say 2j there right? :D

Answer 16

drop the perpendicular!
say X
but XN will not be OD

draw a line parallel to AD from N
let its midpoint be Y

then
XN = XY+YN

now XY is 2j
and YN is OD
:)

Answer 17

PX as always is EO

Answer 18

XY is DN-EP = 10j -8j

Answer 19

Is Y O?

Answer 20

no, Y lies on the line OM
10 units away from O

Answer 21

Directly below P?

Answer 22

it won't be directly below P, right ?
(directly below P, we have put X)

Answer 23

No, wait. I'm confused.