Question

Find this difficult :/

Answer 1

http://screencast.com/t/4UE89MSTZo

Answer 2

@mathmale @eliassaab @Nurali @cwrw238 @Compassionate @Vincent-Lyon.Fr @theEric

Answer 3

help needed only fr the third part :)

Answer 4

@ParthKohli @AccessDenied

Answer 5

So what have you attempted so far? Have you already applied the aforementioned perpendicular distance formulas and found the distances?

Answer 6

What I had done first was use the parameter lambda (I labelled it p because it is easier to type):
r = (1+2p)i + (1+p)j + (2p-1)k
and directly applied the perpendicular distance formula given to each plane. They are equal, so you simply have to solve for the parameter p in the end... and make sure to take care of the absolute values by using both positive and negative cases.

Answer 7

which one did u equate it to?

Answer 8

The perpendicular distance between point r = (1+2p) i + (1+p) j + (2p-1) k and the plane x + 2y - 2z = 1
equals
The perpendicular distance between point r = (1+2p) i + (1+p) j + (2p-1) k and the plane 2x - 2y + z = 7.

Answer 9

And solve for P u get two answers ? then find distance for each P

Answer 10

Yep. The absolute values will give you two answers. And then once you find p for each, you just plug them back into your original line r = (1+2p) i + (1+p) j + (2p-1) k because that gives you the two position vectors of the points. Take their distance to get the final answer. :)

Answer 11

according to the given formula, to which one shuld i plug in the lambda equation?

Answer 12

The lambda equation is the position vector x_1 i + y_1 j + z_1 k
Your plane is ax + by + cz = d

Here is an example for how I set up the first one:
TO x + 2y - 2z = 1
distance = | a*x_1 + b*y_1 + c*z_1 - d | / sqrt(a^2 + b^2 + c^2)
distance = |(1+2p) + 2(1+p) + -2(2p-1) - 1|/sqrt(1^2+2^2+2^2) and then simplify like terms.

Answer 13

thanks il do it and let u know

Answer 14

there is only one value for lambda o.O

Answer 15

What was the value of lambda?

Answer 16

5/2

Answer 17

Hm.. when you simplify that first perpendicular distance down:
|1+2p + 2+2p - 4p+2 - 1| / sqrt(9)
|2p+2p-4p +1+2+2-1|/3
|0 + 4|/3 = 4/3
You got this one?

Answer 18

yes

Answer 19

sorry lambda = 3

Answer 20

Yup, that is one value.
Did you get |-8+4p|/3 for the second?

Answer 21

I mean for the second distance, not second lambda **

Answer 22

Because those absolute values must be kept there to solve this equation:
|-8+4p| / 3 = 4 / 3 <==> |-8 + 4p| = 4 There are two cases, either the inside is positive or negative 4, because then the absolute value of +-4 = 4

Answer 23

which means lambda is either positibe or negative

Answer 24

Well we split it into two cases of the argument, the argument involving lambda has to be positive or negative 4 although not necessarily lambda itself:
-8 + 4p = 4 OR -8 + 4p = -4
Because if the argument equals + or - 4, the absolute value of the whole argument equals 4.

Answer 25

oh okay got that part...thanks yeah :)

Answer 26

appreciate ur help :)

Answer 27

You're welcome! Always glad to help. :)

Answer 28

Then the last thing to do after that is simply substitute each value of lambda into the original position vector:
r = (1+2p)i + (1+p)j + (2p-1)k p=1, 3
and find their distance by the regular distance formula sqrt((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2). :D

Answer 29

yeah :)