3. Find the cosine of the angle between the line L1 passing through P1(1, 4, 2), P2(3, -1, 3) and the line L2 passing through Q1(3, 1, 2), Q2(2, 1, 3).

Q: Show that one of the lines givenby 6x² - xy - 12y² = 0 coincides with one of %3D the lines givenby…

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Q: 5) Find the angle between the lines. y+2 %3D z-5 2x – 3 = y + 9 = 2z + 7 & x +1 = | 2 2.

A: Putting the value of drs of line , we can get angle

Q: 2. The midpoint of the line segment between Pi (x, y) and point P2 (-2, 4) is Pm (2, -1). Find the…

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Q: Find the angle between the lone respected by 2x2+xy-6y2+7y-2=0

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Q: Determine the angle between the two lines: 1₁: 7 = (1,0) + t(0, —2), t ¤ R x+2 y-3 and 1₂: *+² = −³.…

A: Given

Q: Find the angle between the lines x+3y-1=0 and 2x+3y-5=0

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Q: -(39) is the value of a so that the line r 2 – 3t, y = 1 + at, z = -3 + 9t is z +5 x + 1 y + 2…

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Q: Show that the equation of the pair of lines bisecting the angle between the pair of bisectors of the…

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Q: 1. Find the distance between the points P = (-1,3) and Q = (4, -2). Find the midpoint of the line…

A: Consider two points Px1, y1 & Qx2, y2 Then, the distance between the points PQ is given by:…

Q: Use the methods of chapter twelve to find the angle between the 3x lines y 3 and 5x – 2y = 10. - 4

A: In the above question we have given the equation of two lines and we have to find angle between…

Q: 5. Find the bisectors of the angles between the lines, 2x-y 1 and 11x +2y= 5.

A: Given, lines, 2x-y=1,  11x+2y=5 now find angle bisectors between lines we know the formula of…

Q: Find the equation of the plane through P(4, 3, 6) and perpendicular to the line joining P(4, 3, 6)…

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Q: Let P,(1,2, 1)and Pz = (4,2,4). a. Find the direction of the P,Pz b. Find the midpoint of line…

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Q: Find the angle between the curves 4. у%3Dх and у%3х° +х-8

A: First find the intersection point of the curve then calculate slope of tangents of both the curve at…

Q: lem 17. What multiple of a = (1,1,1) is closest to the point b= (2,4,4)? Find also the poin st to a…

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Q: 1. Find the angle between the lines L,:x = 3 + 8t, y = -6t,z = –7+ 24t and L2:x = 3 + 8t, y = 15t, z…

A: Solving only ques 1 according to guidelines.

Q: 2. Find the angle between the lines 3x – 5y = 11 and 6y – 10x = 3.

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Q: (39) is the value of a so that the line r = 2 – 3t, y = 1+ at, z = -3 + 9t is z +5 x +1…

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

A: Answer

Q: 5. Determine the angle 0 between the lines 3x + 4y - 6 =0 and 2x + 3y + 4 = 0.

A: Here we have to determine the angle θ between the lines 3x+4y-6=0 ..................... (1) and…

Q: Find the angle of inclination of the line y-x 1

A: As per the company guidelines we are supposed to solve first question only. Kindly post the other…

Q: 6- Find the distance from the Point AC,2,1) to the line joining the too Points B Co,5,2), C(3,2,7)

A: fghk

Q: O Find the distance from the point (2, 1, 4) to the line r = (-t,6 – 2t, 8 – t).

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Q: The points P, Q and R have coordinates (8, 7), (−2,−1) and (−6, 5) respectively. Show that the…

A: The point P is (8,7) and find the equation of the line passing through the point (8,7).The line…

Q: Let a(t) = (- 5, 5, – 2)t + (8, 1, – 2) and b(u) = (- 3, – 1, 4)u + (- 8, – 6, - 5). Find the acute…

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Q: 1. Find the distance between the points P = ( - 1, 3) andQ = (4, - 2). Find the midpoint of the line…

A: Given :  P = ( - 1, 3) and Q = (4, - 2) we have to find the distance between the points also find…

Q: Find the obtuse angle formed by the lines x+3y+3=0 and x-y-2=0.

A: Topic - angle between lines We will take absolute value of angle as sign depends Up on which line we…

Q: 3. Find the angle from the first line to the second: x – 4y =7 & 3x +5y = 4

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Q: Find (i) the undirected distance between point A and b, and (ii) the midpoint of the line segment…

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Q: What is the equation of the circle concentric with circle(x-2)2 + (y+1)2 = 5 that is tangent to the…

A: Explanation of the answer is as follows

Q: B. Find the line through the point p(1,4) with an inclination V3

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Q: Let a(t) = (– 5, 5, – 2)t + (2, 4, 6) and b(u) 3 (- 3,0, - 4)и + ( - 2, — 8, — 5). Find the acute…

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Q: Find the equation of bisector of the acute angle between the lines 3x – 4x + 7=0 and 12x + 5y – 2 =…

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Q: Find the angle between two lines whose direction cosines are given by l + m + n = 0 and 1² + m² - n²…

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Q: Find the DC’s of the line that is perpendicular to each of the two lines whose directions are and

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Q: Find the angle between the lone respected by 2x2+xy-6y2+7y-2=

A: Given that, 2x2+xy-6y2+7y-2=0

Q: Suppose the angle formed by the line y = 8x and the positive x-axis is 0. Find the tangent of 0. >…

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Q: Find the acute angle between the lines 7x - 4y = 0 and 3x - 11y + 5 = 0.

A: This question is based on straight line.

Q: If point A is reflected over the y -axis and its original location was (2,3), where is its new…

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Q: 4. Find the line(s) containing the point (–1,4) and lying at a distance of 5 from the point (6,3).

A: (Note: We are entitled to solve only one question at a time) To Find: The lines containing the point…

Q: Suppose ABC is reflected across the line x = -1. What are the coordinates for the image of A?

A: There is no change in y coordinates while taking mirror image across x = k.

Q: 1. Find the angle between the lines L1:x = 3 + 8t, y = -6t, z = -7 + 24t and L2:x = 3 + 8t, y = 15t,…

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Q: 1. For the points (3, - 7) and (- 1, 2), find the distance d between the points and the midpoint M…

A: According to our guidlines we can solve only first question 1. Given point 3,-7 and  -1,2To find:…

Q: What are coordinates of AABC with A(-4,3), B(3,1), and C(2,-5) after a reflection over the line y=x?

A: The coordinates of triangle ∆ABC are A-4, 3, B3, 1 and C2, -5To find the reflection over the line…

Q: find the angle between the planes Sメ4y-21。メーマy ト

A: Given the equation of two planes 5x+y−z=10x−2y+3z=−1

Q: Find the angle of inclination of the line y -x = 1

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Q: Use the methods of chapter twelve to find the angle between the 3x lines y = * 3 and 5x – 2y = 10. 4

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Q: Find the z-coordinate of the foot of the perpendicular from A(1, 1, 1) on the line joining B(1, 4,…

A: We will solve the problem.

Q: Let I be the line (1, -1, 1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l.

A: In a 3 dimensional space, a point and a line can be at infinite number of distance from each other,…

Q: 1. Find the angle between the lines L1:x = 3 + 4t, y = 2 – 3t, z = 12t and L2:x = 8t, y = 2 – 15t, z…

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