r-4 Let l be the line with symmetric equations = -- 4. Let P be the point (1, 2, -3), which is not on the line l. Find an equation of the plane containing both l and P, in point-normal form. Hint: Take a point on the line ( where all sides of the symmetric equations are equal to 0.

Q: Consider the lines given by L(t) = (-8, 8, 1) +t(-3, –9, –8), -00 <t< o∞ and M(s) = (-45, –31, – 23)…

A: We rewrite the two lines as

Q: = 2+ 12t Let l1 : 7 = (-1, -5, –4) + t(-16,12, 20) and l2 : = -1– 9t = -5 – 15t (a) What is the…

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Q: b0 = 12, b1 = 0, b2 = -5a. determine whether the plane slopes upward, slopes downward, or is…

A: a).Direction of the slope of a plane:If the sign of the partial slope is positive, the plane slopes…

Q: ) a) Find the point at which the given lines intersect: b) Find an equation of the plane that…

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Q: (a) Find the point at which the given lines intersect. r= (1,3, 0) + t(3, -3, 3) r = (4, 0, 3) +…

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Q: The third question: Let Q be a point in space (1-,1-,1-) and let us have the line L whose equation…

A: For the solution follow the next steps.

Q: I = 10+ 2s I - 1 y +3 12 – z Consider the lines defined by the equations &1 : and l2 : y = 5s 7 z =…

A: Given the lines defined by the equations l1 : x - 15 = -y + 37 = 12 - z9 and l2 : x = 10 + 2sy = 5sz…

Q: b0 = 0, b1 = 0, b2 = 3a. determine whether the plane slopes upward, slopes downward, or is…

A: (a)Direction of the slope of a plane:If the sign of a partial slope is positive, the plane slopes…

Q: x =1- 2t y = 2+3t I: The plane x+2y+2z=3 and the line are parallel z=2-21

A: Since, you have posted more than one question, we solve the first one for you. For the remaining…

Q: y - 2 -1, 3 z - 1 2. Suppose the symmetric equations of lines l1 and l2 are 2 2 - y = z and a = 2…

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Q: Which of the following are equations for the plane through thepoints P(1, 1, -1), Q(3, 0, 2), and…

A: The plane passing through the points P1, 1, -1, Q3, 0, 2 &amp; R-2, 1, 0. Equation of a plane…

Q: hnd an equation of the plane through the point (1,5,4) and perpendicular to the line x =1+ 7t ) y=t,…

A: we have to find the equation of the plane through the point (1,5,4) and perpendicular to the line…

Q: 26. b) Given four points A(-2, 0, -3), B (1, -2, 1), C (-2,-3,2), D ,0). Find the equation of the…

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Q: y? A curve in the xy-plane is defined by the equation + - 3x + 2y = -. Which of the following…

A:

Q: x – 1 y +1 Let the point A = (-1,3,3 ) be the lines r:X=(1,1,-2)+t(2,-1,2) ,teRand s: +2 Determine:…

A: r=(1,1,-2)+t(2,-1,2); a1=2i-j+2k s:x-12=y+1-3=z+2; a2=2i-3j+k A(-1,3,3)

Q: b0 = –3, b1 = 4, b2 = 6a. determine whether the plane slopes upward, slopes downward, or is…

A: It is given that the y-intercept and partial slopes of the plane are –3, 4, and 6 respectively.

Q: b0 = 6, b1 = -2, b2 = -1a. determine whether the plane slopes upward, slopes downward, or is…

A: a)Direction of the slope of a plane:If the sign of a partial slope is positive, the plane slopes…

Q: b0 = 5, b1 = 2, b2 = 7a. determine whether the plane slopes upward, slopes downward, or is…

A: (a)Direction of the slope of a plane:If the sign of a partial slope is positive, the plane slopes…

Q: T = -2+3s Consider the lines defined by the equations l1 : x – 2 = y – 1 = z + 4 and l2 : {y = -1+8…

A: To find the point of intersection of two lines we equate the values of x and y in two lines to find…

Q: (a) Find the point at which the given lines intersect. r = (3, 2, 0) + t(2, –2, 2) r = (5, 0, 2) +…

A: Consider the equations of lines

Q: z-1 Suppose the symmetric equations of lines l4 and l, are = 2 – y = z and x = -1, = 2 respectively.…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: The third question: Let (1-, 1-, 1-) Q be a point in space and let us have the line L whose equation…

A: Let the equation of the plane passing through the point Q-1,-1,-1 be ax+1+by+1+cz+1=0…

Q: Let A = and B = , P = (9, 8, 7) d. find an equation for the plane which contains the point Pand is…

A: We have to find an equation for the plane which contains the point P(9,8,7) and is parallel to A =…

Q: 2: -1+t, y: 3+24, 019:0) show thet the lines う: 4-2t2 CAre parallel. b) Find th plane the determines…

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Q: Find the point, P, at which the line intersects the plane. x= - 2+ 2t, y = - 3 + 8t, z= - 10+ 4t; 7x…

A: We have to find out the point of intersection

Q: 3) The line L: x = 3 + 2t, y = 2t, z = t intersects the plane x + 3y -z = -4 in a point P. Find the…

A: To find the coordinates of P and find the equation for the line .

Q: y = -1+3t and y 5-3s 4 t 2+4s (b) Find the plane that contains these two lines.

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Q: T'he line L: x = 3 + 2t, Intersects the plane x + 3y – z = -4 in a point P. Find coordinates of P…

A: The Line L: x=3+2t, y=2t, z=t Intersects the plane x+3y-z=-4 in a point P Then, (3+2t)+3(2t)-(t)=-4…

Q: Consider the following: a. Write an equation of a plane in Cartesian form that contains the point…

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Q: I = 10+ 2s I - 1 y +3 12 - z Consider the lines defined by the equations ( : and l2: 9. y = 5s z =…

A: We have to find intersection Point of given line and equation of plane which contain both line.

Q: Consider the lines r(t) = (2-3, +4--1) and r(s) (+4,- +3,3+6). A. Show that these two lines…

A:

Q: b0 = 0, b1 = -0.05, b2 = 1.5a. determine whether the plane slopes upward, slopes downward, or is…

A: a).Direction of the slope of a plane:If the sign of the partial slope is positive, the plane slopes…

Q: a) Find an equation of the line in space through the points S(-1,-4,8) and T(2,-1,2). b) Find the…

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Q: c) Find Proj, a. d) Find the equation of the plane (Q) passes through the point Q(-2, 1,0) and is…

A: First calculate cross product of u and v.

Q: I. x+2y+2ze 3 plane and X-1-2+ its line is y= 2+3+ parallel, Z- 2-2+

A: Hello. Since your question has multiple questions, we will solve the first question for you. If you…

Q: Q2. Sketch the three points on 3-D coordinates. Then Find equation of the plane has P1 (3, 2, 1), P2…

A: A cartesian coordinate system contains 3 mutually perpendicular number lines named x axis, y axis…

Q: The line L: x = 3 + 2t, y = 2t, z = t Intersects the plane x + 3y – z = -4 in a point P. Find the…

A: Given: The line L: x = 3 + 2t, y = 2t, z = t intersects the plane x + 3y - z = -4 in a point P.   To…

Q: Q2. Sketch the three points on 3-D coordinates. Then Find equation of the plane has P1 (3, 2, 1), P2…

A: Given points P1 =(3,2,1)P2=(2,1,-1)P3=-1,3,2

Q: T - 1 Y - 2 2-1 Suppose the symmetric equations of lines l1 and l2 are respectively. = 2 - y = z and…

A: Here is some proble for typing these 3d problems. So i solve both the questions with clear…

Q: I(t) = - 2 – 6t Find a plane through the point (6,-5,3) and orthogonal to the line y(t) : = -1-5t…

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Q: 3) The line L: x = 3 + 2t, y = 2t, z = t_intersects the plane x + 3y -z = −4 in a point P. Find the…

A: The equation of the line L is given as x=3+2t, y=2t and z=t. The line intersects the plane x+3y-z=-4…

Q: ) x = 1- t , y = 1 + 2t , z = 2 - 3t Find the equation containing the given line. Then write the…

A: Cross product of any two vector gives a vector perpendicular to the plane containing that two…

Q: x – 1 y + 1 Let the point A = (-1,3, -3 ) be the lines r:X=(1,1,-2)+t(2,-1,2), te R and s: 2 = z + 2…

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Q: The equations of two lines are: L1: r(t) = 2+ t, y(t) = 2+3t, z(t) = 3+t - 3 L2 : 4. (a) Find the…

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Q: O4) Find the eg of the plane that passes throogh) the point (1a) ERpependutar to eauh of Hhe the.…

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Q: Q4/ Show that the lines intersect and find the equation of the plane they determine. L1: X = -1+ 4t…

A: Answer

Q: an equation of the plane that passes through the given point and is perpendicular to the Point…

A: Please refer to the image below

Q: 3. What are the quadrants of the standard (x, y) coordinate plane below that contains the points on…

A: Explanation of the answer is as follows

Q: Pr. #1) Find an equation of the plane. Contains the line = = z+ 2 and is orthogonal to the line r =…

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Q: Pr. #2) Find an equation of the plane. Contains the line r+3 = = and is orthogonal to the line r…

A: