# Finding coordinates given vector eqns and point

• Feb 15th 2013, 11:14 PM
Tutu
Finding coordinates given vector eqns and point
How do I do this,

Point A(3,0,-2) lies on the line r=3i-2k+ t(2i-2j+k) where t is a real parameter. FInd the coordinates of one point which is 6 units from A, and on the line.

I put the equation of the line to parametric form and then, subtracted A from these parametric equations.. but I dont know what I am doing really.

THank you so much!
• Feb 16th 2013, 01:26 AM
chiro
Re: Finding coordinates given vector eqns and point
Hey Tutu.

Hint: Try getting your line in terms of L(t) = a + n*t where n is a unit vector with length 1 and a is your starting point you are starting from and note that for some value t, it will be exactly t units in the direction of n from a.
• Feb 16th 2013, 02:38 AM
Tutu
Re: Finding coordinates given vector eqns and point
Thanks but isn't it already in terms of a+N*t with r=3i-2k + t(2i-2j+k)?
• Feb 16th 2013, 04:05 AM
Plato
Re: Finding coordinates given vector eqns and point
Quote:

Originally Posted by Tutu
Point A(3,0,-2) lies on the line r=3i-2k+ t(2i-2j+k) where t is a real parameter. FInd the coordinates of one point which is 6 units from A, and on the line.

If $A: (3,0,-2)~\&~D: <2,-2,1>$ then let $U=\frac{D}{\|D\|}$.

Define $\ell(t)=A+t\cdot U$. Then your answer is $\ell(\pm6)$ WHY?