Let Lz be the line passing through the points Q1=(-2, -4, 3) and Q2=(1, -2, 4) and let L2 be the line passing through the point P=(-14, -11, -2) with direction vector d-[4, 2, 2]". Determine whether L, 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: 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: 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: 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: 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 two vectors v1 and v2 whose sum is ⟨−3,5⟩, where v1 is parallel to ⟨1,−1⟩ while v2 is…

A: Given Data: The sum of vector v1 and v2 is <-3,5>. The vector v1 is parallel to the vector…

Q: Find the distance between line 1, and the plane parallel to it and containing line I, where 4:…

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Q: Write down the equation of the line that passes through the points (5, -1, 2) and (3, 1, 1). Using…

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Q: Find two vectors v1 and v2 whose sum is ⟨−5,0⟩, where v1 is parallel to ⟨5,1⟩ while v2 is…

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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: 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: 10

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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: Give the equation of the line in vector form, parametric form and symmet The line through the point…

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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: Give the vector equation of the line passing through P and Q

A: To find the equation of the line passing through P and Q.

Q: Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find The equation of the line through (1,2,3) with…

A: Given vectors u=(1, -3, 5)  v=(2, 1,-3)  And line passing of point (1, 2,3)

Q: photo is attached

A: Given informationVector V = (-3, 5)

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 scalar equation of the line perpendicular to (x, y) = (5, 2) +r(1, -3) through the point (2, -2)…

A: The scalar equation of a line is of the form Ax+By+C=0

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: The vector with terminal point at P(-5,0,3) and initial point at Q(6, 2, –8) is equal to 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: The vector equation for the line passing through the points (-4, 1,0) and (4, 4,-3) is r(1)-

A: It is given that the line passes through the points (-4,1,0) and (4,4,-3). Consider that the vector…

Q: Show that direction vectors of the lines 2 - 2 and L: are orthogonal.

A: The given lines are x-32=y+14=z-2-1  and x-35=y+1-2=z-32. The direction vectors of the given lines…

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

A: Given: Let A(7,6,2) and B(2,14,2) be the two points the line passes through To find: vector equation…

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

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Q: Find the equation of the line that passes through the point (3,4,5) and is parallel to the vector…

A: The equation of a line that passes through the point: x0, y0, z0 is L=x0, y0, z0+ta, b, c, where a,…

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 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: 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: 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: Find two vectors vj and 2 whose sum is (-2, -5), where is parallel to (-3, 4) while vz is…

A: Solution: The objective is to find the vectors

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: Find two vectors and īz whose sum is (-4, -2), where vy is parallel to (-2, -5) while ū, is…

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Q: Determine the vector equation for the line that is parallel to = [1,5,-7]+[2,-1,5] with the same…

A: The general equation of line in vector form is    .Then note the result : Line passing through the…

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 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