In: Advanced Math

In this question you will find the intersection of two planes using two different methods.

You are given two planes in parametric form,

- Find vectors n1 and n2 that are normals to Π1 and Π2 respectively and explain how you can tell without performing any extra calculations that Π1 and Π2 must intersect in a line.
- Find Cartesian equations for Π1 and Π2.
- For your first method, assign one of x1, x2 or x3 to be the parameter ω and then use your two Cartesian equations for Π1 and Π2 to express the other two variables in terms of ω and hence write down a parametric vector form of the line of intersection L.
- For your second method, substitute expressions for x1, x2 and x3 from the parametric form of Π2 into your Cartesian equation for Π1 and hence find a parametric vector form of the line of intersection L.
- If your parametric forms in parts (c) and (d) are different, check that they represent the same line. If your parametric forms in parts (c) and (d) are the same, explain how they could have been different while still describing the same line.
- Find m=n1×n2 and show that m is parallel to the line you found in parts (c) and (d).
- Give a geometric explanation of the result in part (f)

Question: (a) Find parametric equations for the line of
intersection of the planes given by 3x − 2y + z = 1 and 2x + y − 3z
= 3.
(b) Find the equation of the plane orthogonal to both of these
planes and passing through the point (−2, 1, 1).

Find the parametric equations of the line of intersection of the
planes x − z = 1 and y + 2z = 3. (b) Find an equation of the plane
that contains the line of intersection above and it is
perpendicular to the plane x + y − 2z = 1.

How there are 3 possibilities for the intersection of 2
planes?

Give an arc-length paramaterization of the line which is the
intersection of the tangent planes of z=x^2+y^3 at (1,-1,0) and
(1,2,9)

Find the equation of the plane through the point (1,1,1) which is perpendicular to the line of intersection of the two planes x−y−3z=−1 and x−3y+z= 2.

Multivariable calculus
Evaluate: ∮ 3? 2 ?? + 2???? using two different methods. C is
the boundary of the graphs C y = x2 from (3, 9) to (0, 0) followed
by the line segment from (0, 0) to (3, 9).
2. Evaluate: ∮(8? − ? 2 ) ?? + [2? − 3? 2 + ?]?? using one
method. C is the boundary of the graph of a circle of radius 4
oriented counterclockwise

Two teams in a laboratory are using different methods of
performing biological tests. Success rate of those tests depends on
the size of the sample material used for the test. The data is
below. In the second column you have success rate for a given size
of a sample. First 10 observations describe success rates of the
first team, while another 10 observations describe success rates of
the second team.
Size
Success
Team 2
Team 2*Size
1
0.219438
0
0...

Explain why it is important for you to understand the different
body directions and planes in reference to the Muscular and
Skeletal Systems. Please post an example\scenario describing
location of bones or muscles using body directions. You may use
quadrants, body cavities (abdominal, cranial, etc.), directional
planes (frontal, sagittal, transverse) and/or
(superior\inferior).

Name two different methods for evaluating evidence. Compare and
contrast these two methods

Using the Internet select two different arbitrators and write a
page about what characteristics you find favorable about them. What
are their qualifications?

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