1. Letz =1+i,1,=-1+i, locate the numbers z+ z, and , vectorially in the rectangular coordinate system.

Q: 1 Suppose a line passes through the point (1, 1 and parallel to the 2' 3 plane x + y + z = 0. Then…

A: The direction vector of the normal to the plane is (1,1,1) Given that the line is parallel to the…

Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find b.…

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Q: Consider the points A(1,-5), B(-1,3) and K(4,-2) in 2D. A. Determine the vector AB B. Determine the…

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Q: 3 2) Determine the vector, parametric and cartesian eguation ef the line passing through-the…

A: Given: Passing point P0(1,3,2) Parallel vector V=(1,1,1)

Q: Г10] Let ÿ = 7 and i = -2. Write y as the sum of two orthogonal vectors, j1 parallel to u and j,…

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Q: التاريخ 5.1 1 1 If the vector [42] An with the straight Piecel the end point?

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Q: 2. The plane containing the point P(Xg» Yor Zo) and having the normal vector n = (a, b, c) is…

A: Equation of a plane passing through the point Px0, y0, z0 and perpendicular to the vector n=a, b, c…

Q: Given the point D(−4, 5, 3) and A = yax + (x + z)z ay, express the D and A in: Kindly answer in…

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Q: Select all possible vector equations for the line through the points (1,1,1) and (3,4,5). OF (t) =…

A: Note that the vector equation of the line passing through two points a→ and b→is given by:…

Q: 4. Find a unit vector that points in the same direction as v = (1,3,9).

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Q: (a) What is the sum V of the twelve vectors that go from the center of a clock to the hours 1: 00,…

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Q: 11. Use vectors to show that the distance from P:(x1, yı) to the line ax + by = c is |ax, + by, – c|…

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Q: 4. Find the vector equations for the line of intersection of the following planes: 2x – y – 5z = -14…

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Q: What is the vector between the point (−3a,−7b) and the point (−4a,−5b)?

A: Vector between two points A and B is B-A

Q: 6. Find the distance of the point (-1,1) to the line given in vector form (x, y) = (2,0) +t(4, 3).

A: Given that: The point is (-1, 1).The vector is:  (x, y)=(2, 0)+t(4, 3)

Q: 4. Given the two vectors rA =-ax - 3ay - 4az and re= 2ax + 2ay + 2 az and point C (1, 2, 3) find: a)…

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Q: 2. If X(-2, -6, 5) and Y(3, -4, 1) are two points in R³ , determine: a) XY b) | XY | in reduced…

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Q: 1 - Find a vector equation and parametric equations for the line segment connecting P(a, b, c) and…

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Q: Let x=⟨1,1,1⟩ and y=⟨0,3,−2⟩Find a unit vector that is orthogonal to both x and y

A: If w is an unit vector which is orthogonal to x and y, so

Q: Give the terminal point of the position vector of u= (3,4). Clearly show why your answer is…

A: Given that Position vector of u→=3,4 So, graphically it is as below:

Q: Q1. If O (0,0,0) in (x,y,z) 3-D space and r(2,5,1) draw the vector in 3D and find its direction.

A: Plot point in 3D

Q: 10.Determine the vector equation of the plane that contains the origin and the intersection of:…

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Q: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: Given vector u = (-1, –1) and v = (-1,1) , determine the value of 5v – u in component form.

A: A vector is a quantity with magnitude and direction. Given a coordinate system a vector can be…

Q: 5. Find the angle between the vectors (approximate to the nearest degree): u = [0, 1,1] and v = [1,…

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Q: linear algebra question:

A: The orthogonal projection is given by,

Q: 2. Let y and u = Write y as a sum of two orthogonal vectors, one in Span{u} and a vector orthogonal…

A: y and u are given to us and we need to write y as a sum of two orthogonal vectors such that one is…

Q: 11) in triple cross of vectors (A × C) × B = Cx (B × A).

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Q: 6. Let y = write y as the sum of two orthogonal vectors, one u = -6 in Span {u} and one orthogonal…

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Q: What is the most general solution to u + v + w = 1, u − w = 2 in vector form?

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Q: Let u=(-2, 0, 1) and v-(-7, -1, 3). Find the value of the j-component in the vector 5u-6v

A: The given vectors are:u=-2,0,1 and v=-7,-1,3First we find the vectors 5u and 6v.

Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

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Q: Consider the four vectors X1 = (0, 0, 0)', X2 = (1, 0, 0)", x3 = (1, 1, 0)", x4 = (1, 0, 1)'. %3D…

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Q: 3. Compute the angle between vector a = (1,2,3) and the positive r-axis.

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Q: Let u = (-1,3) and v = (2, -5). %3D Find the component form of the vector 5u – v.

A: This question is based on resolution into vector components.

Q: 3. (a) Find the terminal point of the vector that is equivalent to u = (2, 3) and whose initial…

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Q: Compute the orthogonal projection of i = 1 onto the line L through 4 and the origin. projz (5) =

A: Vector projection

Q: 1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point…

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Q: and v2 = -3 3. be two -8- Question ( Let vi %3D vectors in R. Show that v belongs to span {v1, v2 }.

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Q: 47. Determine the vector and parametric equations for the line passing through the points P(-1,-3)…

A: We’ll answer the 47th question since we answer only one question at a time. Please submit a new…

Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·¤-A-D-A-A-D 3 +y-2 +2 1 1-2 +3…

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Q: 2.2.12. Prove that two nonzero vectors x, y are orthogonal if and only if |x+y[? = [æ|2 + ly/².

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Q: Find an equation of the plane that passes through the point P(3, 5, 1) and has the vector n = (1, 8,…

A: As we know that; The equation of the plane which is passing through a point Px0,y0,z0 and a normal…

Q: 32. a) Determine the vector equation of the line of intersection of these 2 planes: x + 2y + 2z = -3…

A: According to Bartleby guidelines I can only answer the first question of the given two problems.

Q: Let

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Q: 1.23. Express the unit vector directed toward the point (x, Y, z) from an arbitrary point in the…

A: Express the unit vector directed toward the point (x, y, z) from an arbitrary point in the plane y =…

Q: et x = [7, -4, -8] and y = [-6, -6, –10] be vectors in R'. Compute the following: %3D a+y [ -8x = […

A: Let's find.

Q: 3- Rewrite the vector v in the form a + ib, where vectors a and b have only real components.

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Q: 1. Determine the vector component of A = 3a, + 2ag – 6as tangential to the cone. %3D

A: The vector is A→=3ar+2aθ-6aϕ. Generally, the vectors are shown as sketched below:   Instead of…

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.