Let L, be the line passing through the points Q-(-1, -3, 1) and Q-(3, 3,-1). Find a value of k so the line L, passing through the point P, P,(17, 12, k) with direction vector [2,-3,-31' intersects with L7. K=?

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: Find terminal point Q of vector PQ =    <9, −2, 1>   with the initial point at…

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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: 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: 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: Let f(x, y) = 5y² In(4x). Then Duf(1,4) in the direction of the vector (-2,-2) is

A: The explanation of answer as follows

Q: Verify that it’s possible for a line with direction vector   d=(2,1,-2) to lie flat on a plane with…

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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: Find parametric equations for the line pass- ing through the point P(2, –1, 4) and parallel to the…

A: Given, The line is passing through the point  P 2, -1, 4  and parallel to the vector 1, 4, -2. We…

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: Find a vector equation with parameter t for the line through the points (-1, –7, –4) and (-6, 8, 2).…

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

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Q: 6. Find the distance of the point (-1,1) to the line given in vector form (x, y) = (2,0) +t(4, 3).

A: Given that: The point is (-1, 1).The vector is:  (x, y)=(2, 0)+t(4, 3)

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: Describe all points Q = (a, b, c) such that the line through Q with direction vector v intersects…

A: Given: To Find: All points Q = (a, b, c) such that the line through Q with direction vector v…

Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: we have to represent the line segment from P to Q by a vector valued function and by a set of…

Q: Find the vectorequationof the line of intersection of the planes  2x-3y–z=5 and x+y+2z=1

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

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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: 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: 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: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

A: Given, A line segment passes through the points P1,-1,2 and Q4,1,7 We have, the vector equation of a…

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: If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the…

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

A: Given Points - P1 = -1, 1, 5P2 = 2, 5, 0Vector P1 and P2 ,P1→ = -i+j+5k…

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: Consider the line L with vector equation (x, y, z) = (2,3,0) + t(1, 4, –1). Determine the point on L…

A: Foot of perpendicular is the closest point on the given line, Let M is the foot of perpendicular…

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

A: Given that P1 1, 4, 5   and  P2 4, -2, 7. Compute the direction of vector P1P2 as follows.…

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: Find an equation of the plane that passes through the point P(-3, -2, 3) and has the vector n = (-7,…

A: Find an equation of the plane that passes through the point P(-3, -2, 3) and has the vector n = (-7,…

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: 5) Verify that it's possible for a line with direction vector d = (2,1,- 2) to lie flat on a plane…

A: For the vector representation of a plane , the vectors and lie on the plane. For the equation of…

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: Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.

A: Explanation of the solution is given below...

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: 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: Suppose a line is given parametrically by the equation L(t)=(1-t, t-4, 1-t) then the vector u and…

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Q: 5) Verify that it's possible for a line with direction vector d = (2,1,- 2) to lie flat on a plane…

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Q: Determine the equation for the line with normal vector n = [3,-4] passing through the point P(-1,-2)

A: Given.

Q: Find a vector equation for the line segment from (2, -1, 4) to (4, 6, 1)

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Q: Find a vector that is perpendicular to the graph off (x, y) = 3 + 3x−y at (x, y).

A: Given: fx,y=3+3x-y The normal vector to the given graph can be determined by the gradient of the…

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 points Q, (5,-2, –3) and Q,-(-4, –11, 6). Find a value of k…

A: Equation of line in 3D