The parametric equations for a line L1 are as follows: x = −4+6t y = 2−4t z = 5+2t Let L2 be the line parallel to L1 and passing through the point (3, −2, 3). Find the point P on L2 whose x-coordinate is −6.

Question

The parametric equations for a line L1 are as follows: x = −4+6t y = 2−4t z = 5+2t  Let L2 be the line parallel to L1 and passing through the point (3, −2, 3). Find the point P on L2 whose x-coordinate is −6.

anonymous · Answer

what is the equation that describe L2?

anonymous · Answer

I'm not given one, it just says that L2 is parallel L1 and passes through the point (3, -2, 3)

anonymous · Answer

Yes, you have enough info to find L2

mathmale · Answer

Ian:
L1 is  x = −4+6t y = 2−4t z = 5+2t .  Hidden within this set of equations is the direction vector of L1.  Could you identify that direction vector?  If so, we'll use it as the direction vector of L2.

anonymous · Answer

[-4 2 5] + t[6 -4 2]

mathmale · Answer

You've successfully decomposed the equations for L1 into <-4,2,5> + t<6,-4,2>. The first vector is the vector from the origin to the point (-4,2,5). The second vector is the direction vector of L2. And t is a parameter, only a parameter.

mathmale · Answer

Now that you have the direction vector of L1, how would you write the equation of L2 in vector form?  Hint:  through what point does L2 pass?

anonymous · Answer

would it be <3, -2, 3> + t<6,-4,2>?

mathmale · Answer

Yes, indeed, it would!  Nice work.  Now that you have a formula for x on L2, use it to find the parameter t when x=-6.  Ask for clarification if necessary.

anonymous · Answer

Got it, Thanks!

mathmale · Answer

Really happy you were able to solve this quickly.  All the best to you.  MM