Find an equation of the plane. The plane through the point (7, 5, 4) and with normal vector 3i + j − k   Find an equation of the plane. The plane through the point  (1, −2, −4)  and parallel to the plane 8x − y − z = 4

Q: consider the point A = (-5, -3, 7) and the vector n = a) Which coordinate plane (the x-y plane, the…

A:

Q: Q: Given three points in space P1, -1, 0), Q2, 1, -1),and R(-1, 1, 2), do the following: 1-Find the…

A:

Q: Find the equation of the plane perpendicular to the given vector N and passing through the given…

A: Vector N = (1, 0, -5) and point is given as (5, -1, 3)

Q: Let A(-1, 3, 3), В4, — 1, 0), С(5, 4, —7), and D(2, —1, —1). Find i. the normal vector to the plane…

A: We have to find the normal vector.

Q: (a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), Q(2, 0, -1), and…

A:

Q: 3) Find equations for the lines: a 21 g. The line through (0.-7,0) perpendicular to the plane…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: (a) The line lı passes through the point A (0, 1, 2) and is perpendicular to the plane x - 4y - 3z=…

A: The answer is given below:

Q: Let A = and B , P = (9, 8, 7) c. find an equation for the plane containing A and B and the point P.…

A:

Q: (i) The lines 4, :r = 2i – j+4k + 4(8i+8j+ck) and l½:r=i+k+ u(2i+j) intersect. (a) Find the value of…

A: (a) To find: The value of c and the position vector of the intersection. Given information: The…

Q: (a) Given the vectors u = (0, 6, –2, 3) and v = (1,–1, –1, –1), and the point Xo = (-1, 1,0, 2) in…

A:

Q: Consider the plane that passes through the point P (0, 4, 0) and contains the vectors (2,0, 1) and…

A: Plane equation

Q: Let r1=x1i+y1j+z1k, r2=x2i+y2j+z2k and r3=x3i+y3j+z3k be the position vectors of points…

A:

Q: 2. A plane is defined by the equation 2x - 5y = 0. a. What is a normal vector to this plane? b.…

A:

Q: The planes I and I, have equations II. : 6y+5z =-19, 5 I,:ニx-4y+7:=1. State the normal vector of the…

A: We have to find the normal vectors of the given planes.

Q: Fibe the graph of the equation. = (7 – 21) i + 10tj r = O It is a line in 2-space through the point…

A:

Q: Find parametric equations for the normal line to the surface at the indicated point. (Recall that to…

A:

Q: x- 2. Find a vector equation of a plane that contains the line y+2 -2 and the point A(1,2,1).

A:

Q: Q7. a) Consider the vectors u , v and w are defined by u = i+j ,v = i+ 4j and w = 4i – 3j i. If the…

A: Given :

Q: Find the scalar equation of the line i = [-5,3] + t[2,7]. Тext Find the vector equation of the plane…

A:

Q: Given points A(8, –5, 4) and B(-2, 3,2), find: (a) the distance from A to B; (b) a unit vector…

A: The given points are A8,-5,4 and B-2,3,2. Calculate the values are: (a) The distance from A to B…

Q: The vector equation of two lines , and 4 are 1+x 2- -3+2 and 4 a-y= Given that/, and /, intersect at…

A: Solution (i): Value of a Given lines are, (1+x)/2​=(2-y)/3​=(−3+z)/4​=(r1​)(say)     .... (i)So,…

Q: The solution set to the linear equation 5 · x + y + 4· z = -3 is a plane in 3 dimensions. (a) Write…

A:

Q: Given point A (6,5,8) and plane p with the equation 3x + 2y + 5z = - 24. a. Point A is on the plane…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 2. Given 4(2,–1, 1), B(-1,0,1), and C(-1,-1, 2) а. Parametric equation of the line through A and C…

A: Given:-   A(2,-1,1), B(-1,0,1), and C(-1,-1, 2)  To find C. Equation of  plane that contains the…

Q: 2. Given 4(2,-1, 1), B(-1,0,1), and C(-1,-1,2) Parametric equation of the line through а. A and C b.…

A: Given that: A(2, -1, 1), B(-1, 0, 1), and C(-1, -1, 2)

Q: Find parametric equations for the line that passes through the point P and is parallel to the vector…

A:

Q: 47, 47, 2t) he plane he l and the plane P. Write your answer as a point (a, b, c) whe 9 between the…

A: Given, The line l is represented by nullPlane P is represented by 2x+4y+5z=6. The intersection point…

Q: a) Find an equation of the plane P. b) Consider a vector ũ = (2,-1, 1). i) Show that the vector u is…

A: Fehftig Jj

Q: - pont) The equation of a plane is [x, y, z] = [3, 1, 3] + s[-1, 1, 2] + f[2, 1, 1]. Find a normal…

A: The objective is to find a normal vector to the plane.

Q: Find parametric equations for the line that passes through the point P and is parallel to the vector…

A:

Q: Let å = and b= 3 a) Find the area of the parallelogram formed by the two vectors. b) If the two…

A:

Q: 2. 3. 10,6,-31 You can now find the equation of the plane that contains the point (4,-1.3) and is…

A:

Q: Find the vector equation of the plane that contains the line = [2,0,5] + t[2,-1,3] and passes…

A:

Q: Find a vector perpendicular to the plane that contains the points  P(1, 0, 0), Q(2, 0, −1), and…

A: Three points are given, We have to find the equation of the plane contains the given three points.…

Q: 5. a. Find the equation of the plane passing through the points A(1, –2, 5) and B (2, –10, 9) with…

A:

Q: Given points A(8, – 5, 4) and B(-2, 3, 2), find: (a) the distance from A to B; (b) a unit vector…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: Solve the following vector problems and parametric equations: a) Find the vector equation and the…

A: Q. Vector eqn of line passing through Prx0,y0,z0      and parallel to x, y , z is          r = Pr +…

Q: Q2 a) Find the parametric equation of the line that passes by P(1, 2, 2) and that is parallel to the…

A: We have to solve above question of vector and 3D.

Q: A plane P, in R'is perpendicular to the vector n = (8, 0, 8), and contains the point (4, - 9, - 4).…

A:

Q: (a) Given the vectors u = (0,6, -2, 3) and v = (1, –1, –1, –1), and the point xXo = (-1,1,0, 2) in…

A: Note:- As per our guidelines, we can answer the first part of this problem as all are different…

Q: (b) Consider the three points A(2,3, 1), B(-3,2,2) and C(1, –1,3), as well as the plane P defined by…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: onsider the points below. Р(1, 0, 1), Q(-2, 1, 3), R(6, 2, 5) (a) Find a nonzero vector orthogonal…

A: (b) Consider the value of, a⇀×b⇀=0i+22j-11ka⇀×b⇀=02+222+112=484+121=605=24.59

Q: 16. Find the vector and Cartesian equation of the planes containing, a. the point 4(1,5,3) and…

A: applying vector equation formula for plane

Q: Find parametric equations for the lines i: 1. The line through the point P(3, -4,-1) parallel to the…

A:

Q: Describe the graph of the equation. r = (7 – 21) i + 10r j | O It is a line in 2-space through the…

A: The given equation is: r(x,y)=(7-2t)i+10tj⇒x=7-2t    y=0+10t

Q: (2, –1, -1). Find Let A(-1, 3, 3), В(4, - 1, 0), С(5, 4, -7), and D(2, -1, -1). Find i. the normal…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 25. A plane passes through the point (1, 2, 3) and is perpendicular to a straight IHe IH the…

A:

Q: Q7. a) Consider the vectors u , v and w are defined by ,v = i+ 4j and w = 4i – 3j i. If the initial…

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

Q: Find parametric equations for the normal line to the surface at the indicated point. (Recall that to…

A: Let fx,y,z=x2-9xyz+y2+7z2. and given point is P1,1,1. Partially Differentiating f with respect to…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.