Find a parametrization of the line in which the planes x + y...

Find a parametrization of the line in which the planes x + y + z = -1 and x + z = 1 intersect. Find the parametrization of the line. Use a point with z = 0 on the line to determine the parametrization. x = , y = , z = , -? < t < ?

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Transcript

00:01 We are given here the planes are x plus y plus z is equal to minus 1.

00:08 Let's say this equation first and x plus z is equal to 1.

00:13 Let's say this equation 2.

00:15 We need to find the parameterization of the line in which the planes intersect.

00:20 So basically first of all putting z is equal to z is equal to 0.

00:27 What we will get x will be equal to 1 and x plus y will be equal to minus 1.

00:32 And when we put x equal to 1 in this equation we will get 1 plus y is equal to minus 1.

00:38 Y will be equal to minus 2.

00:40 So point is nothing but equal to here x is 1 y is minus 2 z is was already 0.

00:50 Now we need to find the direction of plane.

00:54 So basically direction of a plane is equal to n1 cross n2 and here what is n1.

01:05 N1 is the direction of first plane.

01:07 So first plane was actually x plus y plus z is equal to minus 1.

01:11 It means the coefficient of x y z is 1 1 1.

01:14 Okay this is n1.

01:16 N2 is a direction of second plane.

01:18 Second plane was x plus z it means 1 comma 0 comma 1.

01:22 So if we find here n1 cross n2 what we will get here...

Question

Find a parametrization of the line in which the planes x + y + z = -1 and x + z = 1 intersect. Find the parametrization of the line. Use a point with z = 0 on the line to determine the parametrization. x = , y = , z = , -? < t < ?

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