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Chapter 3: Q22P (page 112)

Find the angle between the given planes.

2x-y-z=4and3x-2y-6z=7

Short Answer

Expert verified

The angle between the planes θ=35.3.

Step by step solution

01

Concept and formula used

The angle formed by the planes and the normal to the planes is same.

To determine the angle between the vectors by using the formulaθ=cos-1A×B|A||B|.

02

Find the angle

The given planes are,2x-y-z=4 and 3x-2y-6z=12.

Calculating gives the values as below:

A=A=(2)2+(-1)2+(-1)2=6B=B=(3)2+(-2)2+(-6)2=7A×B=(2)(3)+(-1)(-2)+(-1)(-6)=6+2+6=14

Now find the angle:

θ=cos-1A×BAB=cos-1147×6=cos-126=35.3

The angle between the planes θ=35.3.

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Most popular questions from this chapter

Question: For each of the following problems write and row reduce the augmented matrix to find out whether the given set of equations has exactly one solution, no solutions, or an infinite set of solutions. Check your results by computer. Warning hint:Be sure your equations are written in standard form. Comment: Remember that the point of doing these problems is not just to get an answer (which your computer will give you), but to become familiar with the terminology, ideas, and notation we are using

6.{x+y-z=13x+2y-2z=3

Write each of the items in the second column of (9.2)in index notation.

Note in Section 6 [see (6.15)] that, for the given matrix A, we found A2=-I, so it was easy to find all the powers of A. It is not usually this easy to find high powers of a matrix directly. Try it for the square matrix Min equation (11.1). Then use the method outlined in Problem 57 to findM4,M10.eM.


For each of the following problems write and row reduce the augmented matrix to find out whether the given set of equations has exactly one solution, no solutions, or an infinite set of solutions. Check your results by computer. Warning hint: Be sure your equations are written in standard form. Comment: Remember that the point of doing these problems is not just to get an answer (which your computer will give you), but to become familiar with the terminology, ideas, and notation we are using.

7.

Let each of the following matricesM describe a deformation of the ( x , y)plane for each given Mfind: the Eigen values and eigenvectors of the transformation, the matrix Cwhich Diagonalizes Mand specifies the rotation to new axes(x',y')along the eigenvectors, and the matrix D which gives the deformation relative to the new axes. Describe the deformation relative to the new axes.

(2-1-12)
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