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Vectors maths question

The first part I got done was easy couldn't do the second one... Help much appreciated
a) the points A and B have position vectors 2i +j +3k and 4i +j +k respectively line has equation 4i+6j +u(i+2j-2k) show the line through A and B does not intersect with l
b) the point p, with parameter t, lies on l and is such that angle PAB=120 show that 3t^2 +8t+4=0 and hence find position vector of p
Original post by Abeer Ayyaz
The first part I got done was easy couldn't do the second one... Help much appreciated
a) the points A and B have position vectors 2i +j +3k and 4i +j +k respectively line has equation 4i+6j +u(i+2j-2k) show the line through A and B does not intersect with l
b) the point p, with parameter t, lies on l and is such that angle PAB=120 show that 3t^2 +8t+4=0 and hence find position vector of p

Position vector of p is 6i + 4j
Original post by Abeer Ayyaz
The first part I got done was easy couldn't do the second one... Help much appreciated
a) the points A and B have position vectors 2i +j +3k and 4i +j +k respectively line has equation 4i+6j +u(i+2j-2k) show the line through A and B does not intersect with l
b) the point p, with parameter t, lies on l and is such that angle PAB=120 show that 3t^2 +8t+4=0 and hence find position vector of p


The way to go about this is to use the dot product AP.AB = |AP|x|AB|cos(120)= -|AP|x|AB|/2, then rearrange and solve for t. Hope this helps
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Abeer Ayyaz
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Original post by TauBilly
The way to go about this is to use the dot product AP.AB = |AP|x|AB|cos(120)= -|AP|x|AB|/2, then rearrange and solve for t. Hope this helps

Can you please explain how to find the vector AP?
Original post by Abeer Ayyaz
Can you please explain how to find the vector AP?


You do the position Vector of p - position Vector of a. You are told that the position Vector of p is on l with the parameter u =t
Reply 5
Avatar for Abeer Ayyaz
Abeer Ayyaz
OP
6
Original post by TauBilly
You do the position Vector of p - position Vector of a. You are told that the position Vector of p is on l with the parameter u =t

That explains it thanks alot!

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