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

Q: Let L₁ be the line passing through the points Q1=(-4, 2, -4) and Q2-(-1, 0, -6) and let L2 be the…

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Q: Find the point at which the given lines intersect: r = + t r = + s

A: I think the equation of the first line is Thus, the parametric equations of two lines are x = 3 +…

Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Which of the follow is the direction vector of the line 7=(2, 1, 3) + t(-7, 1, 6) (7, 1, 6) O(-7, 1,…

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Q: 39. Given a = (3, -4) and b = (1, 2). Find the vector 2 a. (3,4) a. b. 2,4) c. (6,-8) d. (5,-2)

A: From the given statement,

Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: Which of the following vectors is/not perpendicular to the line whose direction vector is (2,-3,5)?…

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Q: The line that is perpendicular to the lines r = ⟨4t, 1 + 2t, 3t⟩ and R = ⟨-1 + s, -7 + 2s, -12 +…

A: The given lines r→=j^+t4i^+2j^+3k^R→=-i^-7j^-12k^+si^+2j^+3k^ Let,  4i^+2j^+3k^=b1→i^+2j^+3k^=b2→ As…

Q: Consider the line that contains the point (2, -3, 5) and that has the direction vector (1, 2, 4). a)…

A: Given: The line passing through the point 2,-3,5 and having direction vector 1,2,4, To find: The…

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

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Q: Let A be the point with coordinates (-2, -1, -1) and let B be the point with coordinates (2, 0, 0).…

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Q: Find the direction of v:v =(7,-2)

A: Given: v→=7,-2

Q: The value of p, so that the lines 17-14 = 3 2p 22 and 2-5 72 3p 1 = intersect at right angle, is…

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Q: Let Lz be the line passing through the points Q1=(1, 3, 1) and Q2=(7, 12, 4). Find a value of k so…

A: We will solve the problem

Q: Find the distance between each pair of points: с) (-4, 1) and (4, 5) d) (x — 2, у —3) and (х + 4, у…

A: Distance between two points Ax1, y1 and Bx2, y2 is, AB=x2-x12+y2-y12

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

A: Here we have to find the equations for the lines,  a) The line through the point P(3,-4,-1) and…

Q: 3. Given two points P(4,0,2) and Q(2,-1,3), find the equations of the vector PQ, the line passing…

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Q: A direction vector of the line passing through the points A (3,-1,-2) and B(-1,2,1) is <-4, 3,3). •…

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

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Q: Let L₁ be the line passing through the points Q₁(-4, 5, −5) and Q₂(−1, 6, –2 and let L₂ be the line…

A: This is a question of 3D geometry and vector analysis.