А) 9/7 B 3/7 3.

Q: write down the equation of the pair of straight lines joining the origin to the points of…

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Q: Find k so that the line through (4, -1) and (k, 2) is a. parallel to 2x + 3y = 6, b. perpendicular…

A: The line passes through the points (4, -1) and (k, 2). Then the slope (m) of this line is: m = [2 -…

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. distance

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Q: A line passing through (0, –3) and is perpendicular to y =;x – 4. х —

A: The given line passing through the point 0,-3 and it perpendicular to the line y=52x-4. Calculation:…

Q: How find the pistance from fant (1,3) and Line y -4

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Q: (B.) Determined by the intersecting lines L1 and L2 L1 : {x = 2t, y= 4- t, z = 3 +t}and L2:{x = 2 +…

A: According to guidelines we solve one question. thanku.

Q: Which of the following lines is perpendicular to the line   y  =  1/2x + 1   and contains the…

A: Consider the given line y=12x+1                                … 1

Q: The distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3-2t ,y=-2t+1 ,z=t is

A: We are supposed to find the distance between the line x =-2+2t ,y=2t+1, z=2-t and the line x=3-2t…

Q: The line perpendicular to y=x+5, passing through the point (3, 2).

A: You know that if you multiply slopes of two perpendicular lines you will get -1. m1 x m2 = -1

Q: Suppose the symmetric equations of lines l1 and l2 are = 2 – y = z and x = -1, 2 3 espectively.

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Q: 2) through: (-1, 5), parallel to y=-9x – 5 4) through: (-3, 4), parallel to y=-- 4 +3 3

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Q: Find the symmetric equation of line L, that passes through the points (1, 8, 9) and (5, 9, 0).…

A: 9

Q: Find the equation of the line through point (3,7,-11) y is perpendicular to the xz-plane

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Q: 4:x=1+21, y =-2+t, z=4-t 1, :x = 5–3s, y= 4- z = 2+

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Q: write down the equation of the pair of straight lines joining the origin to the points of…

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Q: What is an equation of the line that passes through the point (–6, –6) and is paralle to the line x…

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Q: At what point on the line y = b does the line segment from (0,0) to (a,0) subtend the greatest…

A: Consider the given line y=b  and the points (0,0) and (a,0)

Q: Suppose L, is the line through the origin in the direction of u and L2 is the line through the point…

A: For first line L1, the line passes via origin, i.e., 000 and the line is parallel to u=110, so, the…

Q: Two straight lines 3x – 2 y + 5 = 0 and 6x – 4y + 10 = 0 intersect at the origin. are coincident.…

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Q: The distance between point (1,1,5) and the line x=1+t,y=3-t ,z=2t is:

A: Find the distance between point (1,1,5) and the line x=1+t,y=3-t ,z=2t.

Q: 4. Parallelogram RSTU with R(-4,-2), S(-3, 1), T(3, 4) and U(2, 1); translate right 4 and down 3. =

A: Note as per our guideline we are allowed to do 1 question at a time. So please post next other time.

Q: Find the point of intersection of the pair of lines if it exists. (If an answer does not exist,…

A: Solve the both equation

Q: The distanced 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: Do the lines (x, y, z) = (5 + 2t, 3 + 2t, 1 - If not, how do you know? t) and (x, y, z) = (13 – 3r,…

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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: Find the value of a that makes lines u and v parallel. 130° x+ 135 y O 5

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Q: find the distance between the Linel L) through A(I,0,-1), B (-1,)andthe Line (L2) through C…

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Q: B) Find Duf of f(x,y.z) x + y? + 2? - 3 at point(1,1,1)in the direction of point (3,5,-3).

A: Take gradient at given point and take dot product with unit vector for directional derivative

Q: 3. Line ZW is parallel to line XY and line CD intersects both lines. 154° -Y X 3 4. Based on the…

A: Given To Evaluate m∠1 and m∠2?

Q: What value of K will make the lines 2x + 3y -2= 0 and -6x + Ky= 3 perpendicular? Parallel?

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Q: 4. Find the equation of line 4 that is parallel to v=-i+3j+2k and goes through the point (-6,20,1).…

A: Answer is mentioned below

Q: Find x'z ds, where C is the line segment from (0,2,-3) to (6,0,-6) C

A: To find:∫Cx2z dsThe line segment is from 0, 2, -3 to 6, 0, -6

Q: 9. Are the lines parallel, perpendicular or neither. Show work. 4. y3-x+2 3 3x+4y = 4 %3D

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Q: If ∆MNP is reflected across the line y = 2, then translated using the rule (x + y) → (x – 8, y – 1),…

A: We have been given the coordinates of the point P(7, 4) using the rule  (x + y) → (x – 8, y – 1).

Q: Suppose L, is the line through the origin in the direction of u and L2 is the line through the point…

A: We are given two lines L1 and L2 in 3d, and we have to find the closest points x1 , x2 such that the…

Q: Determine if the following lines are intersecting, parallel, or skew. Line 1: x=1, y = 21+1, z = 31…

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Q: Find the relationship between x and y such that the point (x,y) is equidistance from the points…

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Q: Two straight lines 3x - 2y + 5 = 0 and 6x - 4y + 10 = 0 intersect at the origin. are coincident. are…

A: This question is based on straight line intersection.

Q: Consider the points P(-4, 1, 0, 3), Q(0, 3, 1, -4), R(-2, 1, 5, 0). RS PQ is parallel to Find the…

A: Given:- P=(-4,1,0,3) ,Q=(0,3,1,-4) and R=(-2,1,5,0) To find the point S in R4 whose third component…

Q: find point b (x,y) given that M (7,3) is the midpoint of line A(10,4) and b

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Q: Find the distance from the point (3, 1,0) to the line given by symmetric equations *** =-3, y= 1.

A: Given that: The point is: (3, -1, 0) and equation of line is:         x+42=z-3, y=1

Q: Determine Duf (4, – 1,6) for f(x, y,z) = e**y + 4zx³ in the direction of (-3,2,6). %3D

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Q: What is the point at which the lines x = 3 - t, y = 2 + t, z = 5t intersects with x - y + 2z = 9 ? О…

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Q: 9. Solve for x and y that make the lines parallel.

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Q: Find the equaation of the pair of lines intersecting ar (2,-1) parallel to the pair 6x2-13xy-5y2=0

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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: 4:x 3+6r, y =-2+9t,: =1-12t and L:x=-1+4t, y 3+6,-8r

A: We are given L1: x=3+6t, y=-2+9t, z=1-12t. So, L1: x-36=y+29=z-1-12. Thus, a1=6, b1=9, c1=-12. We…

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: 11. C(2, 5), transverse axis horizontal of length 10, conjugate axis of length 4

A: To find the equation of hyperbola given the following conditions: C(2,5) Length of transverse…

Q: Show that the product of the perpendicular distances from the origin to the pair of straight lines…

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