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!

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.

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)?

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

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