Given a linear map L:R-R such that L(1,0,0)=(3,-1),L(0,1,0)=(2,1),L(0,0,1)=(3,0) , then find L(1,-2,3) ? a. (8,-3) b. (5,2) c. (-1,3) d. (3,-3)

Q: Find the intersection of the lines r(t)=⟨1−2t,13+6t,9+8t⟩r(t)=⟨1−2t,13+6t,9+8t⟩ and…

A: Points are:-

Q: Which one of the following is an equation of the line through points P(1,-1, 2, 1) and Q(3, 1,…

A: We have to find an equation of the line passing through points P(1,-1,2,1) and Q((3,1,1,-1)

Q: Find the point at which the given lines intersect: r = + t r = + s

A: I think the equation of the first line is Thus, the parametric equations of two lines are x = 3 +…

Q: x+2 y+1 z-3 and 7 = [4,-2,1]+t[-2c,2,c] Determine the value of c that makes the lines 5…

A: The direction ratio of is:  (4, 5, 3)   The direction ratio of is:  (-2c, 2, c)

Q: Let r¡(t) = (-4,0, –5) + t(0, 1, –3) and r2(s) = (2, –2, 10) + s(2,0, 3). Find the point of…

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Q: Let R denote the rectangle with corners (−1, −2), (4, −2), (4,1), and (-1,1), and let P denote the…

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Q: In the equation of the line                      ⟨x, y, z⟩ = ⟨x0, y0, z0⟩ + t⟨x1 - x0, y1 - y0, z1 -…

A: The given equation for the line is,

Q: • r : (x, Y, z) = (7, 8, 2) + X(-3, –8, 2) %3D 7 – x y – 8 - x y – 8 2 – z • S : -7 -6 4

A: Given query is to find the angle between two line.

Q: 2. For the following pair of equations, determine if they represent the same, parallel, or different…

A: The equation of the first line L1 is r=1, 0, 3+s3, -6, 3 and the second line L2 is r=2, -2, 5+t2,…

Q: a. Let C = C, U C2 where C, is the line segment from (2,0,0) to (3,4,5) and C2 is the line segment…

A: c1: Line segment from (2,0,0) to (3,4,5)The equation is…

Q: D(3, 7) E(6, 1) F(20, 8) Is the line joining D to E perpendicular to the line joining E to F?

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Q: Find the point of intersection, P, of the lines x - 3 y – 3 Z – 6 3 2 2 x – 2 y – 1 z – 7 - - - 4 4…

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Q: Let r₁(t) = (-7, -6, -3) + t(0, 2, -3) and r₂(s) = (5, -10,-5) + s(3, 0, -2). Find the point of…

A: We want to find the point of intersection of the given two lines.

Q: Find the slopes of the lines containing: a) (2, – 3) and (4, 5) b) (3, – 2) and (3, 7) c) (1, – 1)…

A: We know that slopem of line which contain two pointsx1,y1,x2,y2 is given by m=y2-y1x2-x1…

Q: 1. Determine the intersection (if any) of the lines I1: (x, y, z) = (2,0, 9) + s(1, 2, 3), s e R,…

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Q: Find the line of intersection between the lines: +1 and +.

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: Determine the exact distance between lines l1: 7 = (5,–3,7) + s(3,-2, 5) and l2: 7 = (2,-7,9) +…

A: Here both the lines are parallel.

Q: 10. Show that these two lines are coincident. [x, y, z]= [1, 5, -2]+s[1, 7, -3] [x, y, z]=[-3, -23,…

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Q: Y Find S Zdz Such that c is the line which joining A,B,C and D as follows A (o,1) yB (2,1) , C…

A: Here, firstly we have draw the line C with the given points. Then we have to find integration value…

Q: Given a line defined by the equation T (5,-3,2) + (-8,1,4) and that the point P(x, y, −10) lies on…

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Q: a) Find the coordinates of these points. P( R 44 R( 3 b) Plot and label these points. A (3, 4) в (5,…

A: Explanation and Solution is given below...

Q: The distance d of a point P to the line through points A and B is the length of the component of AP…

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Q: 3. Consider the line [x,y,z] = [3,-2,3]+1[-1,2,-3]. Find the intersection points between this line…

A: Step 1:we have R(t)=[x,y,z]=[3,-2,3]+t[-1,2,-3]R(t)=[x,y,z]=[3-t,-2+2t,3-3t] Step 2:for xy plane…

Q: Consider these lines in three-space. ₁: [x, y, z]= [5, -3, 6] + [-4, 1, -2] l₂: [x, y, z] = [3, -8,…

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Q: (-2,5,7) + t(-3, 1,-4) and that the point Given a line defined by the equation T = P(x, y, 15) lies…

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