Let Lz be the line passing through the point P-(10, 1. –10) with direction vector d--2, -2, 3]", and let L2 be the line passing through the point P--10, 21, -6) with direction vector d-[-2,-6, -1]". Find the shortest distance d between these two lines, and find a point Q, on L7 and a point Q, on L2 so that d(Q, Q2)=d. Use the square root symbol 'V where needed to give an exact value for your answer. d = 0 Q1 = (0, 0,0)

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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

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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,…

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Q: Let Li be the line passing through the point P=(-1,-2,-3) with disection vector da-f-1,3,2], %3D and…

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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 unit vector represented by the directed line segment with initial point A (-2,1,1) and…

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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: Let L, be the line through the origin and the point (5, 0, –1). Let L, be the line through the…

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

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Q: A robot begins moving on a linear path at (2,1). When it reaches (5,2), the robot turns 90°…

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Q: Suppose L(5, 4) was reflected across the line y = x then translated along the vector . What is the…

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Q: Suppose a line is given parametrically by the equation L (t) = (1- 3t,3t – 4, -3-t)- Then the vector…

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

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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 the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

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Q: Find the distance of point 4(2-/3,2) from the line that passes through the origin and parallel to…

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Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

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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: 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).

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

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Q: The vector equation for the line passing through the points (-4, 1,0) and (4, 4,-3) is r(1)-

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Q: Find the unit vector along the line joining point (2, 4, 4) to point ( - 3 , 2, 2). A) -0.8703ax -…

A: We can solve this as follows:

Q: Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and…

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Q: Find the vector v in the plane represented by the directed line segment from (4,-3) to (-2,6)

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Q: Calculate the direction of P₁P2 and the midpoint of line segment P1P2- P 1(3, 4, 6) and P 2(6, 0, 1)…

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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…

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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…

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Q: 1. For the cross product between vectors a=[h, -1, 8] and b=[k, 5, 7] to be axb= [-47, -5, 17], what…

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Q: 3. Find the orthogonal trajectory for the family of straight lines passing through (3,-5).

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Q: Let L be the line passing through the point P-(-4, 2, -1) with direction vector d--3, 1, -2] Find…

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Q: Find the orthogonal trajectory for the family of straight lines passing through (3,-5).

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