Author Topic: C4 vectors help  (Read 1145 times)

Offline T.Q

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C4 vectors help
« on: April 22, 2010, 10:37:08 am »
The point A, with coordinates (0, a, b) lies on the line l1, which has equation

r = 6i + 19j – k + t(i + 4j – 2k).

(a) Find the values of a and b.
(3)

The point P lies on l1 and is such that OP is perpendicular to l1, where O is the origin.
(b) Find the position vector of point P.
(6)

Given that B has coordinates (5, 15, 1),
(c) show that the points A, P and B are collinear and find the ratio AP : PB.
(4)


need help in part c with explanation plz
« Last Edit: April 22, 2010, 10:51:45 am by T.Q »
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Offline astarmathsandphysics

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Re: C4 vectors help
« Reply #1 on: April 22, 2010, 11:08:37 am »
2 hours

Offline astarmathsandphysics

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Re: C4 vectors help
« Reply #2 on: April 22, 2010, 01:54:47 pm »
The point A, with coordinates (0, a, b) lies on the line l1, which has equation

r = 6i + 19j – k + t(i + 4j – 2k).

(a) Find the values of a and b.
(3)

The point P lies on l1 and is such that OP is perpendicular to l1, where O is the origin.
(b) Find the position vector of point P.
(6)

Given that B has coordinates (5, 15, 1),
(c) show that the points A, P and B are collinear and find the ratio AP : PB.
(4)
Form the x cooridate6+t=0 so t=-6
a=19+4t=19+4*-6=-5
b=-1-2t=-1-2*-6=11
b)OP perpendicular to l so OP.v=0 where v is tangent vector of l v=i + 4j – 2k
P is on l so P=(6+t)i+(19+4t)j+(-1-2t)j
OP.v=6+t+4(19+4t)-2(-1-2t)=0 so 84+21t=-4
P=(6-4)i+(19+4*-4)j+(-1-2*-4)k=2i+3j+7k

Offline T.Q

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Re: C4 vectors help
« Reply #3 on: April 22, 2010, 01:57:40 pm »
thanx

but i need help in part c
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Offline astarmathsandphysics

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Re: C4 vectors help
« Reply #4 on: April 22, 2010, 02:11:19 pm »
AP=P-A =(2,3,7)-(0,-5,11)=(2,8,-4)
PB=B-P=(5,15,1)-(2,3,7)=(3,12,,-6)
1.5*AP=PB so AP:PB is 1:1.5 or 2:3

Offline T.Q

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Re: C4 vectors help
« Reply #5 on: April 22, 2010, 02:21:59 pm »

thanx :)


+rep
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Offline astarmathsandphysics

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Re: C4 vectors help
« Reply #6 on: April 22, 2010, 02:23:35 pm »
No probs. Will do a page on my website too