Consider a triangle whose vertices are A(2, -3, 4), B(1, 0, -1), and C(3, 1, 2). a. Find vector AB + BC + CA. b. Find  vector BA + AC +CB.

Q: Q1-)B-)Show that the following triangle whose vertices A(1, -1, 0), B(4, -3, 1) and C(2, -4,5) is a…

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 14j as…

A: ANSWER IS GIVEN BELOW.

Q: Consider the lines y = 2x-3, y = x+ intersect to form a triangle. + 4, and y = x + 3. When graphed,…

A: The graph of  given linear equation will be Shaded region show that triangle formed by the given…

Q: Given the points A: (2,4,-3) and B: (2,-3,5), find the vector ā AB

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Q: .If the position vectors of the points A, B, C, D are a = i+j+k, b 2i + 3j, c= 3i+ 5j - 2k, d k-j.…

A: Given:  a=i+j+k, b=2i+3j, c=3i+5j-2k, d=k-j We know that if A=x1i+x2j+x3k, B=y1i+y2j+y3k then…

Q: Given the points D(-8, 7) and C(2, –6), determine the position vector of CD.

A: The given points are C2,-6 & D-8,7. For the position vector CD→, the initial point is C while…

Q: For the vector a,b,c ∈ IR3 a+b+c=0 and ===1 then ?

A: We will first assume a=(a_1,a_2,a_3),b=(b_1,b_2,b_3) and c=(c_1,c_2,c_3).Now will will use…

Q: Given points (-1, 5, 3), (3, -2, 4), and (-1, –3, 2). compute the area of the triangle they…

A: * A,B,C are points then unit vector is →AB×→ACII→AB×→ACIIand area oftringle is 12→IAB×→ACI

Q: Consider the triangle with vertices P(-1, -4, -3), Q(0, –1, –5), and R(4, –3, –-6). Determine the…

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Q: Pls help

A: ABC is an equilateral triangle and D E f are the midpoints of the sides

Q: Consider the triangle with vertices P(3, -4, 0), Q(4, -1, -2), and R(8, -3, -3). Determine the…

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Q: The angle that vector A =2ax+3a,+8az makes with x-axis is 56.14 42.03 76.82 68.19

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Q: Given vectors: A(6.4,3), B(0.4.6) and C(8.2.1) forms a triangle. Find the angle at point B

A: Solution

Q: Pls help

A: Two vectors are equal iff has same direction and magnitude

Q: The points A, B, C and D form a parallelogram. The points A, B and C have position vectors 2i –…

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Q: Given vectors ū = [3,2, –1] and v = [-2,2,4] , calculate the following: %3D %3D a) 2ū + 30 b) ū · v…

A: Use vector properties.

Q: find The angle of the triangle whose vertices are C(1,-2, 2) Points AC-1,0,2) B (2,1,1) A B

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Q: If a = (4, 3, 1, – 2), ß =(-2, 1; 2, 3) tween a and ß. are two vectors in V(R), find the angle be-

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Q: Let a point a = (2, 4, 5). c) Find a unit vector that has the same direction as a.

A: Divide vector to it's magnitude for unit vector

Q: В (4, 3, -1) m A (5,-1,3) m C

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Q: ectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,-4), R(6,-2,-5), and is…

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Q: .If A = 2a, + a, - 3a, and B = 4ax + 2a, – 3a, are vectors, find (a) A· B (b) Á xB (c) Angle between…

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Q: Given the points A: (-4,6,2) and B: (-1,5,-3), find the vector ū AB

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Q: -dA where R is the triangle of vertices (0,0), (1.0) and (0, 1). answer: 0

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Q: Given points P(4,2,-1), Q(2,-4,-1), T(4,3,4) forms the triangle. Find the unit vector that bisects…

A: We will first find the unit vectors along line QP & QT. So that the resultant vector which is…

Q: Use vectors to decide whether the triangle with vertices P(3, -1, -4), Q(4, 2, -6), and R(8, 0, -7)…

A: Given : Vertices of a triangle P(3, -1, -4), Q(4, 2, -6), R(8, 0, -7)   To find : The given…

Q: In the diagram, ABC is an equilateral triangle, and D, E and F are the midpoints of its sides. As a…

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Q: If the position vectors of the points A, B, C, D are a = i +j+k, b = 2i+ 3j, c = 3i+ 5j – 2k, d= k –…

A: The position vectors of points A, B, C and D are a=i+j+k,  b=2i+3j,  c=3i+5j-2k  &  d=k-j. Now…

Q: Graph each figure and its image along the given vector. a. AABC with vertices A(2, 6), B(1, 1), and…

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Q: Given points: A = (4, 9, 1) B = (-2, 6, 3) C = (6, 3, -2) Using angles between located vectors,…

A: the given vertices are if the dot product of any two vectors is zero then we can say that A, B, and…

Q: . Prove that the figure with the coordinates given is a parallelogram. (Use diagonals bisect each…

A: Note : A & C are diagonally opposite points  And, B & D are diagonally opposite points.

Q: Let a = (- 3, 2) and b = (2, – 5). Find the angle between the vector, in degrees.

A: Given:           a→=-3, 2 and b→=2, -5 We know that the dot product of two vectors is defined as…

Q: Find the angle between in the two planes a = (1,2,3) and b =(4,-5,6)

A: Let's find angle between two plane.

Q: Is the following statement correct? If A, B, C, and D are distinct nonzero vectors represented by…

A: A, B, C, and D are distinct nonzero vectors represented by arrows from the origin to the points A,…

Q: The angle that vector A=2ax+3a,+4az makes with x-axis is 68.19 56.14 76.82 42.03

A: We have to find the angle between vector A and X axis.

Q: For the triangle with vertices located at A(5,3,5), B(2,4,4), and C(1,1,1), find a vector from…

A: The midpoint of AB is obtained by taking the average of the coordinates of the points A,B.

Q: Given the vectors a = (−2, −5, −3) and b = (1, −4, 2), find 1.  5a − 1/3 b. 2. The length of a.

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Q: - Find the lengths of triangle ABC using vectors, knowing that: A (3,1), B (6,4), C (-1,3)

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: If A=(4,3,0), B=(2,3,4) and C= (5,6,2) find the dot product and find the angle between the vectors .

A: A=4, 3, 0B=2, 3, 4C=5, 6, 2 REMEMBER A·B=ABCosθ⇒θ=Cos-1A·BAB

Q: If A=(4,3,0), B=(2,3,4) and C= (5,6,2) find the dot product and find the angle between the vectors.

A: Dot product defined as  AB =|A| |B| cos x x is angle between A and B

Q: Given three vectors A, B, and C as follows, A = a, + a,2 – a 3, В 3 — а,4 + а,, С 3D а,5 — а,2, find…

A: Please see the explanation below

Q: Suppose that A, B, and C are vertices of a triangle and that a, b, and c are, respectively, the…

A: Let A=(x1,y1,z1)B=(x2,y2,z2)C=(x3,y3,z3)

Q: Find the coordinates of the orthocenter of a triangle with vertices at each set of points on a…

A: Given that: (1, 5), (6, 10), (0, 16)

Q: The area of the parallelogram with vectors R(1,2,-1), P2(4,2,-3), P3(6,-5,2).P4(9,-5,0) is a) 998 b)…

A: Consider the given vectors P11,2,-1,P24,2,-3,P36,-5,2, and P49,-5,0. Use the given vectors and draw…

Q: Given points: A = (4, 9, 1) B = (-2, 6, 3) C = (6, 3, -2) Using norm of located vectors, prove that…

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Q: Let a = (- 2, - 3) and b = (4, - 4). %3D %3D Find the angle between the vector, in dégrees.

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Q: 3. Evaluate y dA, where D is the triangle with vertices (2,0), (1,2), and (0, 2).

A: The question is from Advanced Calculus

Q: 6. Show that the points A, B and C with position vectors d = 32 – 4) – 4k, b = 2î – ĵ + k and & = î…

A: To show that the points A,B and C with a given position vectors forms a right angled triangle.

Q: In the following diagram, the rectangle ACEG is divided into four congruent rectangles. F E a) List…

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Q: Given vectors: A(6,3,2), B(1,5,6) and C(6,2,0) forms a triangle. Find the length of the altitude of…

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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.