1. ## vector problem

a man lives on the peak of a hill overlooking the city, where he obsererves the daily routine of three tranportation services, he lables 1, 2 and 3. using the station as the origins he observes each carriage movement relative to the three origin( 0,0)

on a particular day he observes a plane leaving the point of the origin at station 1 at 07:30hrs the plane was located at the point (tan theata{i }+j) i dont know how to write the mathematical symbol for theata. i am asked to find the distance in its simplies form, traveled by the plane in the thirty minute period.

now on the same day he observes the position of two buses, given by the following vectors x=(T+1)i +3j and y=i=(t-1)j, where t is a real number, am now asked to find the values of t for which the buses given by x and y are parallel..

i would like to see how this question is solved so i can try a similar one given to me... am use to vectors in its simpliest form

2. Originally Posted by sigma1
a man lives on the peak of a hill overlooking the city, where he obsererves the daily routine of three tranportation services, he lables 1, 2 and 3. using the station as the origins he observes each carriage movement relative to the three origin( 0,0)

on a particular day he observes a plane leaving the point of the origin at station 1 at 07:30hrs the plane was located at the point (tan theata{i }+j)(Could you clarify this part ? write in words ) i dont know how to write the mathematical symbol for theata. i am asked to find the distance in its simplies form, traveled by the plane in the thirty minute period.

now on the same day he observes the position of two buses, given by the following vectors x=(T+1)i +3j and y=i=(t-1)j, where t is a real number, am now asked to find the values of t for which the buses given by x and y are parallel..

i would like to see how this question is solved so i can try a similar one given to me... am use to vectors in its simpliest form
For part (2) , when 2 vectors are parallel to each other , one can be expressed as a scalar multiple of the other . IN this case ,

x=cy , where c is a scalar

(t+1)i+3j=ci+c(t-1)j

comparing , t+1=c ---1 , 3=c(t-1) --- 2 , solve them .

OR

Since they are parallel , their gradients are equal .

set them equal , and solve for t .

(Bold is to indicate sth is a vector , else it would be a variable)

For part (2) , when 2 vectors are parallel to each other , one can be expressed as a scalar multiple of the other . IN this case ,

x=cy , where c is a scalar

(t+1)i+3j=ci+c(t-1)j

comparing , t+1=c ---1 , 3=c(t-1) --- 2 , solve them .

OR

Since they are parallel , their gradients are equal .

set them equal , and solve for t .

(Bold is to indicate sth is a vector , else it would be a variable)
sorry i just learnt the latex for this, could you actually work the problem so i have a clear understanding,if it not too much of a problem.

on a particular day he observes a plane leaving the point of the origin at station 1 at 07:30hrs the plane was located at the point $\displaystyle tan\theta i+j($Could you clarify this part ? write in words ) i dont know how to write the mathematical symbol for $\displaystyle \theta$. i am asked to find the distance in its simplies form, traveled by the plane in the thirty minute period.

4. Originally Posted by sigma1
sorry i just learnt the latex for this, could you actually work the problem so i have a clear understanding,if it not too much of a problem.

on a particular day he observes a plane leaving the point of the origin at station 1 at 07:30hrs the plane was located at the point $\displaystyle tan\theta i+j($Could you clarify this part ? write in words ) i dont know how to write the mathematical symbol for $\displaystyle \theta$. i am asked to find the distance in its simplies form, traveled by the plane in the thirty minute period.
ok , i will try to work on what we have here . Are you given the velocity vector ? Else , use v to denote that .

Initially , the plane is at x=$\displaystyle \tan \theta$ i+j , do u know how to calculate |x| ?

|x|=$\displaystyle \sqrt{\tan^2 \theta+1}=\sqrt{sec^2 \theta}$

After 30 mins , the plane will be at

$\displaystyle \sec \theta+\frac{1}{2}$v

5. Originally Posted by sigma1
sorry i just learnt the latex for this, could you actually work the problem so i have a clear understanding,if it not too much of a problem.
I think i have worked out almost everything for you , except for the solving part . Which part of my working that you do not understand ?

When you are given two vectors , and you are also told that they are parallel , what can you infer ?

6. i will see how best i can work the equation. any probs i will post again .