find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(1, 4, 5) P2(4, -2, 7)

Q: Let Q be a point in R°. Consider a line passing through P with direction vector d.What is the…

A: Given :- Let Q be a point in ℝ3. Consider a line passing through P with direction vector d→. To…

Q: Which of the following vectors is parallel to the line 7x+ 14y = 20? %3D (-6,3) (8,-16) (2,4) 0.…

A: We first find the slope of the line using y=mx+b form

Q: The vector equation for the line segment that joins the point P(1, 3, –2) to the point Q(2, – 1, 3)…

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Q: Given the points A(-8, 2, 3) and B(-8, 2, -4). Question 3 b) Find the intersection of the line…

A: Question 3.The given points A-8,2,3 and B-8,2,-4.

Q: Find a and b such that the lines r1 = (1, 2, 1) + t(1, −1, 1)andr2 = (3, −1, 1) + t(a, b, −2) are…

A: Given: r1=1,2,1+t1,-1,1 r2=3,-1,1+ta,b,-2 r1 and r2are parallel only if a1=b-1=-21

Q: Given the points P(-3, 4) and Q(-1, 5), express the vector PQ in terms of i and j.

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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: a) Find the vector that is parallel to the tanget to the circle x2 +y? = 100 at the point (3,4).

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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: Let A= (1,2,4), B=(4,1,5), C=(4,2, 6), D=(7,1,7) Find the exact distance between the lines AB and…

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

Q: Which vector has an x-component with a length of 4? -5 A. C B. b C. d O D. a PREVIOUS 19 10

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Q: Find the direction vector of the line joining the points (a) A(7, 6) and B(-2,5), (b) with position…

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Q: Given the points Q(-5, –4) and P(-3,7), determine the position vector of PQ. Select the correct…

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Q: Let P,(1,2, 1)and Pz = (4,2,4). a. Find the direction of the P,Pz b. Find the midpoint of line…

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Q: Q. 6: Suppose the sides of polygon represent vector arranged head to tail. Calculate the sum of…

A: Given: the sides of polygon represent vectors arranged from head to tail. To calculate: the sum of…

Q: For the points P = (- 4, 3) and Q = (5, - 1) write the vector v represented by the directed line…

A: For the points P = (- 4, 3) and Q = (5, - 1) Now we find vector V represented by the directed line…

Q: В (4, 3, -1) m A (5,-1,3) m C

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Q: Given the following ordered pairs: A(-2, 2), B(-2, –4), C(4, 4), and D(4, –2), what vector describes…

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Q: Let P(1,2,1)and P2 (4,2,4). a. Find the direction of the P,P2 b. Find the midpoint of line segment…

A: Find the direction And find the mid point

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: If à = 2a, + 2a,y – a, and B = 3a, + 2a, – 6a, are vectors, find (a) Ả ·Ē (b) Ả × B (c) Angle…

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Q: Given three points P (1, 4, 6), Q (-2, 5, -1)  and R (1,  -1, 1) Find a vector perpendicular to the…

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Q: Given the points Q(-5, –4) and P(-3,7), determine the position vector of PQ. Select the correct…

A: The position vector PQ=Q-P

Q: Let a(t) = (- 5, 5, – 2)t + (8, 1, – 2) and b(u) = (- 3, – 1, 4)u + (- 8, – 6, - 5). Find the acute…

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Q: find the length and direction (when defined) ofu * v and v * u. u = -8i - 2j - 4k, v = 2i + 2j + k

A: Given vectors - u = -8i-2j-4kv = 2i+2j+kPart (1) - u×v = -8i-2j-4k×2i+2j+ku×v =…

Q: For the line that contains the points P(-1, 2, 4) and P2(3, 4, 7), find a) a direction vector. b) an…

A: The line contains the points P1-1, 2, 4  and  P23, 4, 7. a). Direction vector is, P1P2→=3--1, 4-2,…

Q: Given perpendicular vectors a = (5,3,-1) and 6=(2,2,k), find ||||.

A: Given perpendicular vectors a→=5, 3, -1,     b→=2, 2, k   To Find: b→

Q: Find the equation of the line that passes through the point ( 8, 8, 2) and parallel to the vector .…

A: The vector equation of the line which is passing through the point (h, k, l) and parallel to the…

Q: Find the distance between the skew lines i(t) = (3, 0, – 2)t + (7, 9, 0) and p(s) = (4, – 4, – 5)s +…

A: We have to find the distance between skew lines.

Q: For the line €: (x, y, z) = (5, - 3, 2) + n(1, 2, - 2), find a) a point of the line. b) a direction…

A: Given parametric equation of line - x, y, z = 5,-3, 2+n1, 2,-2x, y, z = 5,-3, 2+1n, 2n,-2nx, y, z =…

Q: Consider V=(6, -3) & W=(-4, 8) Find angle between the two vectors.

A: Recall: Angle between two vectors:     Let a→ and b→ be two vectors then,             cosθ=…

Q: Let P1(1,2,1)and P2 = (4,2,4). a. Find the direction of the P1P2 b. Find the midpoint of line…

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Q: Determine the intercepts of each plane. a) [x, y, z] = [1, 8, 6] + s[1, –12, –12] + t[2, 4, -3]

A: As per policy, only the first question is answered as you have asked multiple questions asked in a…

Q: 2. Hhe live in Passing through He oryun and haring * l as it's divecha vector intersects the line…

A: The line in ℝ3 passes through 0 , 0 , 0 and it's directional vector is 1u3. Thus , equation of line…

Q: Set C 1. Use vectors to find the (shortest) distance between the point (-2, 1, 4) and the line…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 4) Which of the following vectors is parallel to the line L: x = 1 -t, y = 2 + 3t, z = 5 + 2t? a)…

A: According to the guidelines we are answering first question. Please repost the remaining.…

Q: For what value(s) of k are the vectors ü (2k, 5, k) and v = (3, -8, k) perpendicular

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Q: Let Q be a point in R. Consider a line passing through P with direction vector d.What is the…

A: Let Q be a point in ℝ3. A line L passes through point P with direction vector d→

Q: Let / be the line through the point with coordinates (-1,2,0) in the direction of the vector Which…

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Q: Given the points F(-7, 1) and E(-2, –7), determine the position vector of EF. Select the correct…

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Q: For the line €: (x, y, z) = (2, 3, 4) + n(3, - 2, 5), find a) a point of the line. b) a direction…

A: the given line is: l:x,y,z=2,3,4+n3,-2,5 we have to find: (a) a point of the line. (b) a direction…

Q: For what values of a and B will the vector (a, 1, B) be orthogonal to (4, 0, 3) and (-1, 1, 2)? a =…

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Q: Given the points P(4, 4, 3), P(1, 4,0) and P3(10,0, 2). Find the vector that is orthogonal…

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Q: Let / be the line through the point with coordinates (-1,-2,-1) in the direction of the vector Which…

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Q: Find an equation for the line through P(11,10) parallel to vector v=2i-3j

A: Given point on the line is P(11,10) The vector parallel to the line is,v=2i-3j

Q: find the length and direction (when defined) ofu * v and v * u. u = i + j - k, v = 0

A: Consider the given vectors and rewrite vector v in terms of i, j and k. u=i+j-kv=0v=0i+0j+0kTo find…

Q: Find the component form of the specified vector. The vector PQ , where P = (3, 3) and Q = (-6, -4) O…

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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.