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Chapter 3: Q3P (page 112)

In Problems 1 to 5, all lines are in the (x,y) plane.

3. Write, in parametric form [as in Problem 1], the equation of the straight line that joins (1,-2)and (3,0).

Short Answer

Expert verified

The parametric equation of line is (3i)+(i+j)t.

Step by step solution

01

Concept of the straight line in slope form.

Write the expression of slope.

y-yox-xo=m ………… (1)

Here,m is the slope andx0 andy0are the coordinates.

02

Substitute the values in slop equation 1 and 2

First point is(1,-2) and the second point is(3,0).

Substitute -2 for y0,1 for x0,0 for y12 and 3 for x1, in equation (1).

0-(-2)3-1=mm=1

Substitute 0 for yo, 3 for xo, and 1 for m in equation (1).

y-0x-3=1y1=x-31

Thus, a=1 and b=1 in parametric form.

03

Substitute the values in parametric form

The parametric form is,x=3+t.

And,y=t.

Thus, the parametric equation can be written as follows:

r=(3,0)+(1,1)t

Therefore, the parametric equation of the line is (3i)+(i+j)t.

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Most popular questions from this chapter

If A=4i-3k and B=-2i+2j-k,find the scalar projection of A on B the scalar projection of B on A,and the cosine of the angle between A and B .

Evaluate the determinants in Problems 1 to 6 by the methods shown in Example 4. Remember that the reason for doing this is not just to get the answer (your computer can give you that) but to learn how to manipulate determinants correctly. Check your answers by computer.

Answer

Step-by-Step Solution

Step 2: Find the determinant.

The objective is to determine the determinant of .

Add two times the third column in the second column, to get

Now, do the Laplace development using the second column to get

Hence, the value of the determinant is .

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

Find AB,BA,A+B,A-B,A2,B2,5-A,3-B. Observe thatAB≠BA.Show that(A-B)(A+B)≠(A+B)(A-B)≠A2-B2. Show that det(AB)=det(BA)=(detA)(detB), but that det(A+B)≠detA+detB. Show that det(5A)≠5detA and find n so that localid="1658983435079" det(5A)=5ndetA.Find similar results for det(3B). Remember that the point of doing these simple problems by hand is to learn how to manipulate determinants and matrices correctly. Check your answers by computer.

localid="1658983077106" A=(25-13),B=(-1402)

Let each of the following matrices M describe a deformation of the(x,y)plane for each given Mfind: the Eigen values and eigenvectors of the transformation, the matrix Cwhich Diagonalizesand specifies the rotation to new axesrole="math" localid="1658833126295" (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.

role="math" localid="1658833142584" (3113)
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