(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

There is points:

P=(1,2,3,4)

Q=(4,3,2,1)

and line L passes through P and is parallel to A

A=(1,1,1,1).

X(t) is anypoint on line L.

1. Find the distance between X and Q as a fucntion of t.

2. Find the minimum distance between Q and the line.(which is 2(5^{1/2}))

2. Relevant equations

Parametric equations....

distance between two points.

3. The attempt at a solution

Im really not sure if my approach is right at all.... i just want to understand where im going wrong.

For 1.

I tried the parametric equation of the line which is

X(t)=P+At

to go from X(t) to Q its

X(t)-Q=(P-Q)+At=(-3,-1,1,3)+(1,1,1,1)t

X(t)-Q=(-3+t,-1+t,1+t,3+t)

the distance between X(t) and Q would be

d=||(X(t)-Q)|| or d=((X(t)-Q).(X(t)-Q))^{1/2}

For 2.

then the distance squared as a function of t would be

d^{2}=(X(t)-Q).(X(t)-Q)

this gives d^{2}=20+4t^{2}

the derivative is (d^{2})'=2((d^{2})'d(^{2}

(d^{2})'=(2(8t)(20+4t^{2})

(d^{2})'=320t+64t^{3}

set the derivative to 0 for minimum and i get

t=(-320/64)^{1/2}

Its clearly not the right answer of 2(5)^{1/2}

I dont know where im going wrong.

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# Homework Help: 4D: mimimum distance between point and parametric line

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