in-exercises-21-and-22-find-a-parametric-equation-of-the-line-m-through-mathbfp-and-mathbfq-cdottext

Question

In Exercises 21 and $22,$ find a parametric equation of the line $M$ through $\mathbf{p}$ and $\mathbf{q} \cdot[	ext { Hint: } M 	ext { is parallel to the vector } \mathbf{q}-\mathbf{p} . 	ext { See the }$ figure below. 
$$
\mathbf{p}=\left[\begin{array}{r}{2} \ {-5}\end{array}ight], \mathbf{q}=\left[\begin{array}{r}{-3} \ {1}\end{array}ight]
$$

Priyanka Sadarangani · Accepted Answer

okay. And this question of figure is given. That is excellent. XTO So p Victor is here. Que victories. Hair minus p is here and a play line and passes through B and Q and resultant off Q minus. B will be here. Okay. And water that, given the data, the P equals two to minus five. Put minus five and cubicles toe minus 31 Okay, on from the hand am is parallel to the vector. Q minus B dissector on from the equation three. The Parametric Rhetoric Question off a line through a parallel to be that will be X equals toe be T Q minus p. Okay, so we help us all this X equals two. We will put the value of a fast be this plus T and Q minus 31 minus beer too. So minus five. Okay, so for solving this, we get X equals two Gu minus five. Bless. Be minus 56 Okay. And that is our final. I&#x27;m set. Thank you.

Runpeng Li · Answer

Okay, So in this problem, working than two vectors, Prospector is selective. Six and three second vector ISS Q, which is zero connected for now, we need to find a line that is passing through both P and acute. So that is to say, we&#x27;re fine. We&#x27;re two people, a line that is passing through P. But at the same time, this lie has to be parallel to Q minus. P has to be parallel to these. Look these factors. So we personally to find out, find out to the Q minus p. So what is this vector? So in this case, cubed minus P minus P is zero naked, four minus connective six and three. So in this case, have six and connective seven. Now, remember, in order to write down the equation of the line that passing through P but parallel to six and next seven, we first right down the point which it is passing, passing through as accounts in terms. So that is, um, we&#x27;re taking P here so that it&#x27;s a negative six and three class. The bacteria wishes, which is parallel to line we&#x27;re looking for. So that is six on detective seven and we need to times time this vector by a skater teas and tease A real number. All right, so this is our, um our equation in vector. For now, we transform this into a paramedic for so that is X one and the expressed as connective six. Last 60 and X two can be expressed as three minus 70 someone. This is our by no answer.

Ethan Somes · Answer

Okay, so here we have two points on the line, and those two points are negative. 23 and for seven. And we want to make a parametric equation for this line. Um, And when tees equals zero, I want to be at this point and when in Tizi Close one, I want to be at this point. So when I&#x27;m writing a pair metrics that equation to this, I&#x27;m gonna have except t And why of TV. Okay, so when Exit East 28 0 I know my ex value has to be negative, too, and it&#x27;s going to feel lying to him. A negative two plus something times T. So I have some amount of change that&#x27;s happening every time, Um, between each t value in my X direction and then in why of t when t zero I needed to be three when there&#x27;s some not change every time. So the change in X from tea is one to t. T zero to tea is one. So that will be It goes from negative 2 to 4. So that is a change of plus six. I&#x27;m so every t we need to add six more, so that Intel&#x27;s in my equation used three x of t negative two plus six t So started negative too. And I add six every time I, um, jump a t. So now why of tea will be three plus What? See? What changed and why is it goes from three to seven? Start adding four so four t here. I&#x27;m sorry. Two equations are here.

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

Linh Vu · Answer

the question on the line. Yeah, having the direction with the V equal to the A B C and upon b x zero advisors Israel, they would have a formula X y Z e Co two extra wiser zero plus 80 plus Piti plus City, in this question, were given the line here having a point 245 and in a perpendicular to the Plan three X Plus seven y minus five z equal to 21. And because the line here is perpendicular to the plan, it means Standard Edition better. We were equal to the normal of it on the plan and equal to the coefficient in front of the X Y Z here could be +37 minus five. And then, with the direction better and the point, we can find the question on the line. It will be X, Y and Z. We have the Jew for five. For the point, we have the narrative photography plus three D plus 70 minus five days

Linh Vu · Answer

it goes by. The question underlines is that is going through the Pont you for five and in this perpendicular job Plan three x Last seven y minus five z go Judah Genting one here with the second information we confined in detention with the genetic Ojeda coefficient in front under X y Z Therefore 103 7 minus five And now we can find a question in the line. We have the X wines here with the point here we have a Jew, Fun five and adoption with the 400 plus three day plus 70 minus five d.

Problem

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

Problem 21 Easy Difficulty

Answer

$x=p+t(q-p)$
$x=\left[\begin{array}{c}{2} \\ {-5}\end{array}\right]+t\left[\begin{array}{c}{-5} \\ {6}\end{array}\right]$

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

Linear Algebra and Its Applications

Catherine R.

Caleb E.

Kristen K.

Michael J.

Absolute Value - Example 1

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$x=p+t(q-p)$$x=\left[\begin{array}{c}{2} \\ {-5}\end{array}\right]+t\left[\begin{array}{c}{-5} \\ {6}\end{array}\right]$

Linear Algebra and Its Applications

Catherine R.

Caleb E.

Kristen K.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

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

Catherine R.

Caleb E.

Kristen K.

Michael J.

$x=p+t(q-p)$
$x=\left[\begin{array}{c}{2} \\ {-5}\end{array}\right]+t\left[\begin{array}{c}{-5} \\ {6}\end{array}\right]$

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

Linear Algebra and Its Applications