equation of a line intersecting two planes

sorry are you trying to find the equation of the line describing where the 2 planes intersect each other?

Its okay, I haven't done this stuff in absolutely ages, so I'm afraid I might not be much help..

is the answer $\lambda(3i + 9j + 14k)$

if its nothing like that I'll leave someone who knows what they're talking about to help..

Hi, thanks

I'm assuming that's a multiple of the direction vector of the line? If so I don't think it's quite right, but perhaps I'm misunderstanding something?

Sorry I'm pretty sure I'm wrong actually. Like I said its been absolutely ages since I did anything like this :L

Perhaps if you go through how you got your answer I (or someone else) could see if it seems reasonable or spot what you did wrong?

x

Sorry I'm pretty sure I'm wrong actually. Like I said its been absolutely ages since I did anything like this :L

Perhaps if you go through how you got your answer I (or someone else) could see if it seems reasonable or spot what you did wrong?

EDIT: Right, I've now done some revision for you.. Your direction vector is the same as what I've now got, and you can check whether your solution is right by picking a value for lambda (anything you like), and seeing if the point you get lies on both planes. if you pick a couple of different values and they all lie on both planes then your solution is correct.

Another thing, while it doesnt really matter, is that for your direction vector, you can write:
h(-6i - 12j - 9k)
as h(2i + 4j + 3k), as h = any number, you can effectively multiply through by -1 to get all of them positive and divide by 3 to make them the smallest integers - Its just the ratio that is important. This is just for neatness though, so if its in any way confusing, ignore me

Just editted my last post - yeah that looks perfect, assuming no mistakes in the calculations you can try putting a couple of values of lambda in to check that the points on your line are on both of the planes to make sure

Hi,

I've got the question:

$plane_1 : \textbf{r}.(5\textbf{i} - \textbf{j} - 2\textbf{k}) = 16$
$plane_2 : \textbf{r}.(16\textbf{i} - 5\textbf{j} - 4\textbf{k}) = 53$

Find the equation of the line intersecting these two planes.

I think these sorts of questions have multiple answers but my textbook only gives one (which is different to mine) does anyone know a way I can check my answer to see if it is correct?

By the way, my answer is:

$(-7\textbf{j} - \frac{9}{2}\textbf{k}) + \lambda(-6\textbf{i} - 12\textbf{j} - 9\textbf{k})$

Thank you

Is this A2 Maths?

Hi,

I've got the question:

$plane_1 : \textbf{r}.(5\textbf{i} - \textbf{j} - 2\textbf{k}) = 16$
$plane_2 : \textbf{r}.(16\textbf{i} - 5\textbf{j} - 4\textbf{k}) = 53$

Find the equation of the line intersecting these two planes.

I think these sorts of questions have multiple answers but my textbook only gives one (which is different to mine) does anyone know a way I can check my answer to see if it is correct?

By the way, my answer is:

$(-7\textbf{j} - \frac{9}{2}\textbf{k}) + \lambda(-6\textbf{i} - 12\textbf{j} - 9\textbf{k})$

Thank you

There will be an infinite number of solutions depending on your choice of a point on the line and the way you write the direction vector.