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Consider the following planes. x + y + z = 4, x + 3y + 3z = 4?

0 votes
Consider the following planes. x + y + z = 4, x + 3y + 3z = 4?

(a) Find parametric equations for the line of intersection of the planes. (Use the parameter t.)
(x(t), y(t), z(t)) =

(b) Find the angle between the planes. (Round your answer to one decimal place.)
asked Feb 7, 2015 in CALCULUS by anonymous

2 Answers

0 votes

(b)

Step 1:

The equations are

.

.

The normal vectors of two planes are

image.

image.

The angle between two planes is

image

image

The angle between two planes is image.

Solution:

The angle between two planes is image.

answered Feb 9, 2015 by Sammi Mentor
edited Feb 9, 2015 by Sammi
The correct angle is

7/sqrt(57) = cos(theta). Then take the inverse of cosine and then you'll have your angle.

22.0 degrees
0 votes

(a)

Step 1:

The equations are

image

image

The cross product of two normal vectors is the direction vector for the line of intersection.

The normal vectors of two planes are

image.

image.

The cross product of two vectors is

The direction vector of line of intersection is image.

Step 2:

Solve the eqn(1) and eqn(2).

Multiply eqn(1) on each side by 3.

.

Subtract eqn(2) from

Substitute in eqn(1)

.

There are no solutions for and .

So, take the point as .

The = is lie on the line of intersection.

The direction vector of line of intersection is image.

The parametric plane equation is

The parametric equation is .

Solution:

The parametric equation is .

answered Feb 9, 2015 by Sammi Mentor
edited Feb 9, 2015 by Sammi

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