Let L7 be the line passing through the points Q-(-1, 2, 5) and Q2-(-4, 1, 3) and let L, be the line passing through the point P=(0, 14, 22) with direction vector d-[-3,-6,-9] Determine whether L, and L, intersect. If so, find the point of intersection Q. The lines intersect at the following point Q: Q = (0.0.0)

Q: Let L, be the line passing through the point P=(8, -6, 0) with direction vector a=-3, 3, 1]", and…

A: Given, L1 is the line passing through the point P1=8,-6,0 with the direction vector d1→=-3,3,1T. So,…

Q: Determine the value of k for which the direction vectors of the lines x+3 Z = y = -1 are…

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Q: Let L7 be the line passing through the points Q1=(5, -5, -1) and Q2=(3, -3, 5). Find a value of k so…

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Q: Show that the lines L1 : x = 4 – t, y= 2t, z = 5+t and L2 : x = 1+4t, y= 3 – 8t, z= 5 – 4t are…

A: Let's find.

Q: Let L1 be the line passing through the points Q1(1, 1, 1) and Q2(4, −5, −8) and let L2 be the line…

A: Given L1 be the line passing through the points Q1(1, 1, 1) and Q2(4, −5, −8) L2 be the line passing…

Q: Show that the lines L1 : x = 5 – t, y = 2t, z = 5+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

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Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(3, 4, 5) P2(2, 3,…

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Q: Find the distance between the line L1 through the points A(1, 0, -1) and B(-1, 1, 0) and the line L2…

A: Given:Find the distance between the line L1 through the points A (1, 0, -1) and B(-1, 1, 0) and the…

Q: Show that a set of vectors {v,, v2. ..., V5} in Rn is linearly dependent when dim Span {v,, v2, ...,…

A: We need to show that: {v1, v2, v3, v4, v5}  in Rn are linearly dependent when  dim Span{v1, v2, v3,…

Q: Find a plane containing the point (6, -4,-3) and the line (t) = +t 270

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Q: Let L1 be the line passing through the point P1=(3, 13, 13) with direction vector →d1=[1, 3, 2]T,…

A: Shortest distance

Q: Let L, be the line passing through the points Q(-3, 2, -5) and Q2-(-6, 4,-4) and let L2 be the line…

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Q: Let L7 be the line passing through the point P1=(1, 3, 7) with direction vector d= [-2, -2, 2]", and…

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Q: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: The given points are The vector QP is So, the unit vector (v) of QP is

Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y-2z=3 is: O0 -3i+6j-3k…

A: Two planes are given: 4x-y+z=2 and 2x+y-2z=3

Q: Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). 7(t) =…

A: The vector equation of a line passing through any two points with position vectors a  and  b is…

Q: Let L₁ be the line passing through the point P₁=(5, 2, 3) with direction vector d=[1, 3, 1]', and…

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Q: Let L7 be the line passing through the points Q1=(3,-5, –1) and Q2=(0, 4, –10). Find a value of k so…

A: Given that L1 be the passing through the points Q1=(3,-5,-1) and Q2=(0,4,-10). And the line  L2 be…

Q: d s: X = (0,1, -1) + λ (1, α, 2α) are coplanar, in which case study its relative position.

A: Consider the given lines. r: X=(1,0,2)+λ (2, 1, 3) And, s:X=(0,1, -1)+λ(1, α, 2α) Let r and s are…

Q: If possible, determine the vector, parametric,symmetrical and reduced line r that: a) passes…

A: Given the lines S1:t·1,2,3, t∈ℝ and S2:y=x+2, z=x. To find a line L passing through the point P1,1,1…

Q: Find the vector equation of the line, L that passes through the points P (2, -2, 8) and Q (10, 8,…

A: Given query is to find the equation of the line passing through indicated points

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(0, 0, 0) P2(2, -2,…

A: To find:(a) the direction of vector P1P2(b) the midpoint of line segment P1P2P1(0,0,0) and…

Q: Let L, be the line passing through the point P(-3,-5,-6) with direction vector d-[1,0,-1]", and let…

A: Line L1 passes through the point P1=(-3, -5, -6) with direction vector d1→=1, 0, -1T. ⇒L1: r→=(-3,…

Q: Let L7 be the line passing through the point P-(-19, –9, –10) with direction vector d=[3, 2, 1]',…

A: Here we find the point q1 and q2 and shortest distance.

Q: Show that the lines L1 : x = 4 – t, y = 2t, z = :5+t and L2 : x = 1 + 4t, y = 3 – 8t, z = 5 – 4t are…

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Q: Suggest a "vector proof" of the fact that, inR2, two lines with slopes m1and m2 are perpendicular if…

A: Given: ℝ2 To Prove that : m1 m2=-1

Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 4 y + 7 = z +…

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Q: 27. Are the points P(1, 2), e(7,3), and R(-2, 1) on the line with vector equation = (19,5) + s(6,1),…

A: According to our terms and conditions I have solved first question for next question repost

Q: Show that direction vectors of the lines x-3y+ 1 L: and 2 -2 are orthogonal.

A: Direction vector of a line x-x1a=y-y1b=z-z1c   is   <a,b,c>  So, Write the direction vector of…

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

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Q: Let L, be the line passing through the point P-(1, -7, 5) with direction vector d-[1,-2, 0], and let…

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Q: Find a direction vector for the line containing the points (-1, 5, 2) and the point (2, 3, - 1).

A: We have to find a direction vector for the line containing the points -1, 5, 2 and 2, 3, -1. We know…

Q: Show that the lines L1 : x = 2 – t, y = 2t, z =1+t and L2 : x = 1+ 3t, y = 3 – 6t, z = 5 – 3t are…

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Q: Find a vector perpendicular to the graph of z = - 3 x2 + 9 y2 – 7 x y at the point (8, 2, -268).

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Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 5 +t and L2: x = 1+4t, y = 3 – 8t, z = 5 – 4t are…

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Q: Show that the lines L1 : x = 3 – t, y = 2t, z = 3+t and L2 : x = 1+ 3t, y = 3 – 6t, z = 5 – 3t are…

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Q: / Determinel the Component of the Vector at each Point (州,) {0r0),(40), (-り),(り, (ー4) ニ…

A: Explanation of the answer is as follows

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

A: Let L be the line through the point with coordinates 2, -1, 0 in the direction of the vector -11-1.…

Q: Let Lz be the line passing through the points Q=(-3, -3, 5) and Q2=(1,-9,–1) and let L2 be the line…

A: Given that the line L1 passes throogh the points Q1=-3,-3,5 and Q2=1,-9,-1The direction vector of…

Q: Let L, be the line passing through the points Q-(1, -4, 5) and Q-(-1,-7, 2) and let L2 be the line…

A: To find: The intersection point of the lines L1 and L2. Given information: The line L1 passing…

Q: let L1 be the line passing through the points Q1=(2,1,1) and Q2 = (-4,10,7). Find the value of k so…

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Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 5+t and L2 : x = 1+ 2t, y = 3 – 4t, z = 5 – 2t are…

A: To show that the lines L1: x=4-t, y=2t, z=5+t and L2: x=1+2t, y=3-4t, z=5-2t are parallel and to…

Q: Let Lz be the line passing through the point P;(2, -5, 4) with direction vector d=[1, 1, 3]", and…

A: Here we calculate the distance between two line using differentiation.

Q: Find the coordinates of a point P on the line and a vector v parallel to the line x = 3 - 5t, y = -1…

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Q: Show that the lines with vector equations L1: 7 = (-2,1,0) + s(1, –1, 1), s ER L2 : 7 = (0,1,0) +…

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Q: If v1, ..., V5 are in R' and v3 = 0, then {v, V2, V3, V4, V5} is linearly dependent. %3D

A: Definition used: v1, v2, ..., vk is linearly dependent if there exist numbers α1, α2, ..., αk, not…

Q: Let Lz be the line passing through the points Qz=(2, 2, -4) and Q2=(8, –-1, 2) and let L2 be the…

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Q: Let L, be the line passing through the points Q, (5,-2, –3) and Q,-(-4, –11, 6). Find a value of k…

A: Equation of line in 3D