Show that the lines px + qy + r = 0 and P1x + q1y +r¡ = 0 are parallel or identical if and only if pq1 – P1q = 0.

Q: Show that the lines 2r + 3y = 1 and 6r - 4y -1=0 are perpendicular.

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Q: Find a and b such that the lines r1 = (1, 2, 1) + t(1, −1, 1)andr2 = (3, −1, 1) + t(a, b, −2) are…

A: Given: r1=1,2,1+t1,-1,1 r2=3,-1,1+ta,b,-2 r1 and r2are parallel only if a1=b-1=-21

Q: 1. Show that the lines having the equations 4x- 3y + 12 = 0 and 8x 6y + 15 = 0 are parallel.

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Q: Show that the lines having the equations 4x – 3y + 12 = 0 and 8x – 6y + 15 = 0 are parallel.

A: According to question,Given equation of lines,4x - 3y +12 = 08x - 6y +15 =0

Q: Given the lines l1 and l2; l1 :x = 1+ 3t, y = 2 - 6t, z = 7t – 3, x - 4 l2 : 6 - y 3 (a) Show that 4…

A: Answer

Q: Consider two lines: l1(t)=⟨6+4t, 8−2t, 2+6t⟩ & l2(t)=⟨1+4t,3−2t,4+5t⟩ a)  Do they intersect? If…

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Q: Determine whether the lines r1(t) = 〈0, 1, 1〉+ t〈1, 1, 2〉 and r2(s) = 〈2, 0, 3〉+ s〈1, 4,…

A: line1:xyzt1+t1+2t and line2:xyz2+s4s3+4sto find the point of intersection we need to equate both the…

Q: The lines y = 2x - 1 and y = ax + 2 are perpendicular ifa = _______.

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Q: Find the product of the lenghts of the perpendiculars drawn from (2,1) upon the lines…

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Q: Determine whether the lines 5x+3y =9   and -3x+5y=10  are parallel, perpendicular, or neither.

A: We know that  Two lines with the same slope are parallel. Two lines whose slopes have a product of…

Q: Determine whether the lines L1 and L2 passing through the pairs of points are parallel,…

A: Slope is basically the vertical or the horizontal change between two distinct points. In a graph,…

Q: 44. Select the pair of lines that are parallel. O 5x – 2y = -1 y = 4x – 1 4x – 6y = 6 2x – 3y = -6 -…

A: two parallel lines is of the form  ax+by=c and ax+by=d where a,b,c,d are constants

Q: If the straight lines ax + by + c=0, bx + cy+ a=0,x+ay+b =0 are concurrent, then prove that a +b+c'…

A: Given straight lines,  ax + by + c = 0 bx + cy + a = 0 cx + ay + b =0 The three straight lines are…

Q: Are the lines = 7+12t, y = 12–10r, z = 1+2t, and.x = 6+13t, y = 8+2t, z = 10–5t parallel? O No O Yes

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Q: Determine whether the given lines are parallel x = 3+ 2t 5 – 4t y = 2-t 1+ 3t 6+ 2t || y = %3D 2 6t…

A: To determine whether the below linear are parallel or not. x=3+2ty=2−tz=1+3t; x=5−4ty=6+2tz=2−6t

Q: 2) Determine whether the lines 1: x = 1+ 2t, y = 3t, z = 2 – t and l2 : x = -1+ s, y = 4 + s, z…

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Q: Determine whether the lines y = 3x - 2 and 2x + 6y = 7are parallel, perpendicular, or neither.

A: Given:          y=3x−2   and 2x+6y=7

Q: Label the follwing lines as parallel, perpendicular, or neither to the line y = 2x - 4 2x + 4y = -12…

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Q: Show that the lines 2 x+3 y-1 and 6 x-12 y-1=0 are not perpendicular

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Q: Consider the two lines L1: x=−2t,  y=1+2t,  z=3t and L2:  x=−9+5s,  y=3+2s,  z=1+5s Find the point…

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Q: Whether the lines 3x+2y=6 and 2x-3y=6 are parallel or perpendicular

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Q: The line that is perpendicular to the lines r = ⟨4t, 1 + 2t, 3t⟩ and R = ⟨-1 + s, -7 + 2s, -12 +…

A: The given lines r→=j^+t4i^+2j^+3k^R→=-i^-7j^-12k^+si^+2j^+3k^ Let,  4i^+2j^+3k^=b1→i^+2j^+3k^=b2→ As…

Q: Show that the lines given by the following equations are parallel. L1: 2x + 3y = 6 L2: 4x + 6y = 0

A: Given: L1: 2x+3y=6L2: 4x+6y=0 Concept Used: Parallel lines have equal slope.

Q: Determine whether the lines L1:(x−22)/7=(y−17)/7=(z−19)/7 and L2:(x+15)/8=(y+22)/9=(z+22)/10…

A: NOTE: Refresh your page if you can't see any equations. . the first line is  write the given line…

Q: Consider the two lines L1: x =-2t, y = 1+ 2t, z = 3t and L2: x =-9+5s, y = 5s, z = 4+ 2s Find the…

A: As the lines intersect thus their components are equal thus equate the components of the lines L1…

Q: Suppose that two lines Re((1+i)z+2i+3) = 0 and Re(2-bi)z+5) perpendicular. then b=. 0 are ||

A: We will convert the equation into cartesian form and then use condition for perpendicular lines

Q: Determine whether the lines L1: (−2, −1) and L2: (1, 3), (5, −5) passing through the pairs of points…

A: Since, we have been given that two lines are L1: (-2,-1), (1,5) and L2: (1,3) , (5,-5). Our Aim is…

Q: Find the product of the lenghts of the perpendiculars drawn from (2,1) upon the lines…

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Q: - Classify the following lines as parallel or perpendicular or neiti a- y=4x-7 & y=4x+9. b- y=-5x+1…

A: Given: a. y=4x-7  and y=4x+9b. y=-5x+1  and y=3-5xc. y=12x and x=12y Concept Used: Two lines are…

Q: E. Show that the lines 3x - 5y + 19 =0 and 10x + 6y -50 =10 are perpendicular and find their point…

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Q: Which of the following lines is perpendicular to the line   y  =  12x + 1   and contains the point…

A: Given line is y=12x+1 And the point is (2, -2)   By comparing the equation of line y=12x+1 with…

Q: What is the general equation of a line given the points P(1,3) and Q(4,7)? O 4x-3y+5=0. O 4x+5y+3=0…

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Q: Determine if the lines ℓ1: x − 9 = −t, y + 4 = 3t, z − 9 = 3t and ℓ2: x − 1 = s, y − 4 = −s, z − 9…

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Q: Are the lines x = 7+11t, y = 11–61, z = 4–9t, and x = 3–12t, y = 7–t, z = 12–6t parallel? Yes O No

A: We have to check whether given line is parallel or not?

Q: 12- Show that the lines L1 and L2 are parallel and also find the distance between them. L1: x=2-t,…

A: Solution: Consider the given lines in parametric form; L1:Consider x = 2 - t = x0+ aty = 2t = y0 +…

Q: Consider the two lines L1 : x= -2t, y= 1+2t, z= 3t and  L2 : x= -5+s, y= 1+4s, z= 1+5s find the…

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Q: Determine whether the lines L, and L, are parallel, skew, or intersecting. х — 1 y - 2 z - 12 %3D 1…

A: Given problem :-     To find:-  Intersection point of given lines

Q: Determine whether the lines 2x + 5y =7 and 5x +2y =2 are perpendicular true or false

A: Compare the equations with standard equation  y=mx+c

Q: Show that the two lines X= 1+4t X = 2 + St and y= 5-4t J= 4 - 36 Z: -1+ SE 2: 5+t Rind the distance…

A: There are two equations of line:

Q: Show that the lines with symmetric equations L1 : = = and L2 : 팡!%3D 부 =D 촬 %3D y-3 are skew.

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Q: Find the product of lenght of the perpendiculars drawn from (2,1) upon  the lines…

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Q: suppose I tell you that the line ax+5y=7 is parallel to the line 4x-2y=11. What is a?

A: Given equation of the line 4x -2y = 11   .......(1)and another line 9x+5y = 7 .....(2)we find the…

Q: 46. If the lines a¡x + b¡y = c1 and a2x + b2y = c2 are %3D parallel, what can you say about the…

A: Topic:- parallel lines

Q: Suppose that the two lines ay= x-y and 2/ax+3y=1 are parallel. What must be the value for a?

A: First of all, consider general equation for the straight line. Also consider the given equations.

Q: Find the product of the lengths of the perpendiculars drawn from (2,1) upon the lines…

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