in-exercises-19-and-20-find-the-parametric-equation-of-the-line-through-a-parallel-to-mathbfb-math-2

Question

In Exercises 19 and $20,$ find the parametric equation of the line through a parallel to $\mathbf{b}$ . 
$$
\mathbf{a}=\left[\begin{array}{r}{3} \ {-4}\end{array}ight], \mathbf{b}=\left[\begin{array}{r}{-7} \ {8}\end{array}ight]
$$

Runpeng Li · Accepted Answer

his problem. We&#x27;re going to find the Parametric equation off the line through when a parallel to vector B. So I&#x27;ll write down point and vector here. Here&#x27;s the point. A is three next four on Vector B ISS connective seven and eight. So to do this problem, we just follow the result given me in the textbook, that is, we write down, we write down the point we&#x27;re passing through as accounts in Victor and we write down the the vector that we that we are required to be parallel to that its neck of 78 as our slope. So that is that is our question for the line. And this line is passing passing through point A, which is three next four and parallel to Vector B, which is a seven and seven and eight Now, bird of war. We can write down the Parametric form, so that is X one because, um, three minus 70 and next to because negative four plus 80 just do the vector addition here. So that is three plus negative seven times the scaler t so that it&#x27;s a negative 70. So that&#x27;s our first equation. The second equation the same well, apply the vector additions That has a negative four plus 80. So that is our second question. So this is our parametric form.

Michael Jacobsen · Answer

in this example, we have a vector, a vector be given. And what we want to do here is to determine the a parametric equation the line that will go through a in the direction of B To do that Well, let x be a vector containing X one and x two, then the our question would take the form X equals a plus T times be where t is any real number. All right, T is in our So the form this takes is the vector X will be equal to first A which is negative 20 plus t times a vector B, which is negative +53 Now, when t equals zero, we find that ex itself becomes just this party here. So our equation, the line will definitely go through negative to zero. And as t varies to be, any real number will be in the direction of this vector B as it multiplies here in that expression. So this is the a parametric equation for the line

Eric Mockensturm · Answer

we&#x27;ll testify. Parametric equations for the curve Why equals nine minus four X, where these air always kind of easy to do because we can always say that say just that that X equals T and enemy of substitute that in here and we get why close of nine minus 40. So that&#x27;s our parameter ization in terms of tea.

Eric Mockensturm · Answer

and this problem. We&#x27;re looking for the Parametric equations for the line that has a slope of eight and passes through the point minus for nine. So we&#x27;re given the slope is eight and a point on the curve, so we can use our formula for a line with the slope given a slope in a point. And that is the slope Times X plus or minus X, not which is minus four. So we get X plus four in here and then plus, why not? Which is nine substituting ex, um, t for X and we get why equals 80 plus 41 so our parametric curve would look like t 80 plus 41.

Eric Mockensturm · Answer

in this case, we are given the points 31 and minus 54 And we want to find a parametric equation for the line that passes through them. So the slope, in that case of the change in why this three and the change in X is minus eight. So we take our slope minus 3/8 and one of the points or take 31 And so we get why equals the slope times X minus X not which is three plus, why not We parameter rise this equation. We can set X equals t and then why equals I actually have a t here. Why equals minus three h T plus 17 8th and then t would range from, um minus 5 to 3.

Linh Vu · Answer

questions, questions off the line, having the direction we ve go to the ABC and that Porn on the line x zero y 00 Then we have the formula X y z ico too extra wiser in zero plus 80 plus B t plus C t. In this question were given the line that&#x27;s going through the pawn be Geico to the minus 203 and upon kill echo to the 35 minus two. Here we can use the Pompey, but you in front of that is what the V and we&#x27;re just equal to the better be kill. And then we tell the Cuban, manage the B. So get Geico Judah 55 minus five. We can get another simple form of the direction, but there will be we divide everything by find every kind of 11 minus one. Now, given we got the dashing better and upon P here we can get the question of the line will be X y Z equal to minus 203 plus the plus the honesty

Problem

In Exercises 21 and $22,$ find a parametric equat…

Problem 20 Medium Difficulty

In Exercises 19 and $20,$ find the parametric equation of the line through a parallel to $\mathbf{b}$ .
$$
\mathbf{a}=\left[\begin{array}{r}{3} \\ {-4}\end{array}\right], \mathbf{b}=\left[\begin{array}{r}{-7} \\ {8}\end{array}\right]
$$

Answer

$x_{1}=3-7 t$
$x_{2}=-4+8 t$

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$x_{1}=3-7 t$$x_{2}=-4+8 t$

Linear Algebra and Its Applications

Heather Z.

Alayna H.

Kayleah T.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Heather Z.

Alayna H.

Kayleah T.

Michael J.

$x_{1}=3-7 t$
$x_{2}=-4+8 t$

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications