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Using the point P 0 = (1, 0, ~2) and the vector v (1,3, -1), do the following: (a) (2pts) Write a parametric vector equation for a line through P 0 in the direction...

Question

Using the point P 0 = (1, 0, ~2) and the vector v (1,3, -1), do the following: (a) (2pts) Write a parametric vector equation for a line through P 0 in the direction of v (b) (3pts) Write the scalar equation for a plane through P 0 with normal vector v: (c) (Spts) Find a parametric vector equation for the same plane you found in part (b): Attach File Browse My Computer Browse Content Collection

Using the point P 0 = (1, 0, ~2) and the vector v (1,3, -1), do the following: (a) (2pts) Write a parametric vector equation for a line through P 0 in the direction of v (b) (3pts) Write the scalar equation for a plane through P 0 with normal vector v: (c) (Spts) Find a parametric vector equation for the same plane you found in part (b): Attach File Browse My Computer Browse Content Collection



Answers

For the following exercises, points $P, Q,$ and $R$ are given.
a. Find the general equation of the plane passing through $P, Q,$ and $R .$
b. Write the vector equation $\mathbf{n} \cdot \overrightarrow{P S}=0$ of the plane at a, where $S(x, y, z)$ is an arbitrary point of the plane.
c. Find parametric equations of the line passing through the origin that is perpendicular to the plane passing through $P, Q,$ and $R$ $P(1,1,1), Q(2,4,3),$ and $R(-1,-2,-1)$

Okay were given. P is going to have one cover for Q is three comma one from the three, and art is negative, too. How about one covers out? Let's find about Pete you that's equal to 50 comma native. One buying back the cute are that's equal to negative $5 0 common negative dreams. Okay, so we know that the cost product pick you and Q arm is without the notables pick you and you are so it's normal to the plane. So let's let and beat a normal vector. This is going to pick you up, Beth. You are. And that's equal to actually this hero cop 20 club. Now let's choose any three given points, right equation the plains. Let's use music. Would you like to come in once before? And we know it no more. Back to zero comma 20. That was out to get their all times exports to 20 times Y minus one several times. Be what it's for. This is equal to don't. So we have that solving this, that this Why is he why this one is? You get to know. So why is it that one? Okay, now for Park day. Let's let s equal X cover White company C in arbitrary points on the plane. No, that p s is equal to experts to comma. Why minus one covers. C'mon, it's sport and I know more back there it is again They're all common 20 comment So in the PS was equal to drop it Here you go Thoughts, experts to come a y minus one comma C'mon, it's sport. It's equal job okay, And now for part c But the key people to ex couple Why would you be any point on the plane? And that's it. Oh God, the origin. So Fulla t is equal to this ex con a wide coming and we know they're normal line and the vectors against our common 20. So we know that lt does it produce some scare multiple of So we get X comma y coming he because he put zero comma 20. So unless we get that excited to go, why people to 20 and the desert or any tea contained it on

The problem is find a Wachter equation on the Parametric equations was a line segment that vice he took you. He appears and saying Q is new. VW. There's a doctor equation This aren't you is the cultural one month steam, much parts water. You see, I asked you cams Good luck to you. He covered. Your key is greater than zero on DH smallest. Why the corresponding Parametric equations are actually cool too A Cam's mom Honesty Plus you, Counsel, this isn't true. You mind pain, Hands to clasp. Why is it good to eat times one dynasty us This is equal to minus house to casting, See is equal to see Tams one Manistee Last W. Thompson, this is Echo two W Manus C comes to us See Andi tease returns and cereal on Smaller than what?

According to the caution, we need to find the equation off the plane. We have given point and a normal vector given point is be not. The value off key note is zero do minus two and the given value normal doctor and is 11 minus one. We know that equation off the plane. He's equation off the plane. He's okay. X minus X north, plus B via I minus. Why not less? See Zed minus zed. Knock. We know that ABC are normal rectors. We have normal vectors. Value 11 minus one. When we substitute this value here, one ex miners we know that X notify nodes that not. It's a point. The value of point is zero to minus toe when we substitute all values. Hill, we have B is von by my nurse. Why no is too lo. See, is minus one zag clothes. They're not who When we sold the execution eggs blows. Why miners do? Minus said my nose do. When we sold this equation we get. The final result is X close by miners. Zed minus four is equal to zero. We get the final question off plane is why miners egg is it will do for

Were given in a bart a point to be not with one comma minus two or more to the and our line Points de Come on, my Nestea Going on duty, We need to find the question off deeply. We know that Artie is a good two x not my Note that note Blessed Day and do A B C. We're ABC are the victors off the plane and excellent this line or they're not, are they? Be not point so that they put devalues er we are having tea comma minus de Goma. Duty music will do one comma minus two comma three Presti and do ABC We need to find out break. So does bring the Steve Value. Here the stick t common your T one comma minus one comma two minus t into a B C is equal to one call minus two Coma three. So we get D one minus a minus one minus. B tu minus C is equal to one comma minus two comma three. So therefore we get one. Minus is it will do the one one minus b is it Will do minus two. Andi, I do minus C is equal. Do three. So it implies is zero B is minus one one on C is equal to minus one. So I get directors as zero comma, one comma, minus one and we're having point, which is one going minus two Go moxie. Now let us use the formula into X minus X Nord plus B in do I minus. Why not? Classy, Indo said, minus that noticeable to zero to find the equation of people in. So we have a zeros. This whole expression will be zero. They just put the value of being witches one by minus minus two becomes plus two plus minus one into zed minus two. The is equal do zero. So why bless to minors? Ed plus three is equal to zero toe. I minus said plus five is equal to zero is a question off the blink we have the but were given be not minus four comma. One homer to similarly R is equal do duty going minus Goudie comma minus four D. So this find the the directors So it is minus for gonna one coming to within the same formula. Bless Dean, you were gonna be going to see we have values as the distinctive woman here. Tu minus two minus four. Let's bring my Nestea. It could become a C is equal to minus one come to. So I get to minus a minus two minus B minus. Pulled minus. C is a good do minus four comma, one common to so to minus A's equal to minus four minus two minus BZ. Good one minus pool minus C is equal to two. The which implies my is it will do. Six. My baby is a girl. Do minus three on my C is equal Do minus six. So therefore I have my in vector as six common minus three. Come on, minus six. You can very prior on the point Be not as minus four comma One comma too. So therefore my question becomes into x minus x not lesbian. Do I minus? Why not Plessy into Zed? Minus said No physical zero. So I get 16 to express Ford minus three. And do Why minus one minus six into zit minus two is equal to zero 66 less 24 minus three. What? Plus three minus six. It last well is a good a zero. So I guess 66 minus three by minus exit bless 39 is equal. Do zero


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