Let Lz be the line passing through the points Qz=(2, 2, -4) and Q2=(8, –-1, 2) and let L2 be the line passing through the point P=(-5, 1, -11) with direction vector d-[-1, 2, -1]". Determine whether L7 and L, intersect. If so, find the point of intersection Q. If not, find a value for the z- coordinate of P, so the resulting lines do intersect.

Q: Find a vector equation for the line through the point (-6, 4, 1) perpendicular to the vectors u =…

A: A line passes through the point -6,4,1 and perpendicular to the vectors u→=-1,-2,3 and v→=3,-8,-9 We…

Q: Find two vectors v, and 02 whose sum is (-5, 5, –3), where 0 is parallel to (-1, –2, 1) while Dz is…

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Q: Let L7 be the line passing through the points Q=(-5, 4, 4) and Q2=(-6, 2, 2). Find a value so the…

A: We will solve the problem

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: Suppose that L1 is the line through point (1, 2, 3) with direction vector [2 ,- 3 ,0]t. And suppose…

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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: Find a vector equation for the line through the point (-3, –1,8) perpendicular to the vectors ū =…

A: vector equation can be find in the following way:-

Q: 2) L is the line passing through points (0, 0, 0) and (1, 1,1). M is the line passing through (2, 3,…

A: Direction vector of the first line is = (1,1,1)-(0,0,0)= (1,1,1) So the equation of the first line…

Q: Let L₁ be the line passing through the point P₁=(-8, 0, 11) with direction vector ₁-[-3, 2, 3]T, and…

A: Given The line L1 passing through the point P1=-8,0,11 with direction vector d1→=-3,2,3T The line L2…

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 a vector equation with parameter t for the line through the points (–1, –7, –4) and (-9, 8, 2).

A: we know that vector equation of line which passes through pointsx1,y1,z1,x2,y2,z2 is given by…

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: 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: 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: Show that direction vectors of the lines 3 L: and

A: We have to find the direction vectors for the lines L1: x-32=y+14=z-2-1 and L2: x-35=y+1-2=z-32.

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

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Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

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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: Find an equation of the plane that passes through the point P(-7,–5,5) and has the vector n = (-1,4,…

A: Given : Point P(-7,-5,5) and a normal vector n=<-1,4,2>   To Find : Equation of the plane that…

Q: Let L₁ be the line passing through the point P₁-(-3,-16, -2) with direction vector ₁-[2, 3, 1], and…

A: Given: L1 is a line passing through P1=-3, -16, -2 with direction d1→=2, 3, 1T and L2 is a line…

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 the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4 r=⟨ ,…

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Q: Find a vector orthogonal to the line x+y=1

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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 Lz be the line passing through the point P-(10, 1. –10) with direction vector d--2, -2, 3]", and…

A: We will use formula for the shortest distance.

Q: The line that passes through the point (4, -2,0) and parallel to the vector (1, 2, –3) has symmetric…

A: The solution is given in the next step.

Q: a) Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4]

A: To find the equation of line.

Q: Let L7 be the line passing through the point P1=(-7,-15, 10) with direction vector d=[3, 3,-2]', and…

A: For skew lines ( lines in space which are neither parallel nor intersecting ) , the line of shortest…

Q: Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the…

A: The transpose component is X=1, -3t

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 two vectors j and 02 whose sum is (-3, -4), where j is parallel to (0, 5) while 02 is…

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Q: Let Lz be the line passing through the points Q1=(-2, -4, 3) and Q2=(1, -2, 4) and let L2 be the…

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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: Find the vector equation of the line (a) through the point (1, −5) and parallel to the x-axis; (b)…

A: As per our guideline we are allowed to do 1 question and 3 subparts at a time. Please post other…

Q: Explain how to find a vector in the direction of the line segment from P0(x0, y0, z0) to P1(x1, y1,…

A: Initial point is P0x0, y0, z0 and the terminal point is P1x1, y1, z1.

Q: Find symmetric equations for the line that passes through the point (5, -2, 7) and is parallel to…

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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: Find a vector u € R' such that, at the point (2, 1, -1), the function f(, v, 2) =-y + 2a2 + has its…

A: Given, f(x,y,z)=-y3+2x2+z2

Q: Find an equation of the line that goes through A(0, 1, 4) and is orthogonal to the Y-axis and vector…

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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 L7 be the line passing through the points Q-(-1, 2, 5) and Q2-(-4, 1, 3) and let L, be the line…

A: This question is related to three dimensional geometry.

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

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Q: Give the vector equation of the line passing through P and Q.P = (1, 1, 0), Q = (1, 0, 1), R =…

A: P=(1,1,0) and Q=(1,0,1)we have to find vector equation of the line passing through these points

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

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Q: Let L be the line passing through the point P1-(-2,-14, 4) with direction vector d=[-1, -3, 2]', and…

A: Solution: Let L1 be a line passing through the point P1=-2,-14,4 with direction vector d1→=-1,-3,2T.…

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