Do the lines (x, y, z) = (5 + 2t, 3 + 2t, 1 - If not, how do you know? t) and (x, y, z) = (13 – 3r, 13 – 4r, 4 – 2r) intersect? If so, at what point?

Q: 2. Find the equation of the plane containing the lines L1: (x-2)/2 = (y+1)/-1 = z/3; L2: (x+1)/2 =…

A: Given that:L1: x-22=y+1-1=z3L2: x+12=y-1=z+23

Q: Q10)The two lines L1: x=3-2t, y=4+t ,z= 6-t and L2: x=5-4t, .y=-2+2t, z=7-2t are parallel

A: 10) The equation of the line x=3-2t t=x-3-2 y=4+t t=y-4 z=6-t t=z-6-1

Q: Determine if the line intersects the plane. If so, state the solution. [x, y, z ] = [− 1, − 9, 16]+t…

A: The given line is [ x, y , z] = [ -1, -9, 16]  +  t   [ 3, 3, -5]  and the given plane is x+4y+3z=11…

Q: raction of the lines 3y - x=2, 2y-5x

A: Given:- 3y - x=2, 2y-5x=7  and  y - 2x=7 To find the equation of the line passing through the point…

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: Verify that the lines are parallel, and find the distance between them L1: x = 2 - t, y= 3 + 4t, z =…

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Q: Sketch the lines 3x+ 4y 7 and x- 2y = 6, and find their point of intersection. Hint: Their point of…

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

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Q: Determine the equations of the line through P(-1,2, 1) and parallel to the line of meek section of…

A: Given P(-1,2,1) and parallel to the line of intersection of the planes 2x+y+z=2, x+2y+z=10

Q: 1. Write the line parallel to y = -2x + 5 that passes through the point (1,1). a. y = -2x + 1 b. y…

A: Question 1 - The equation of line is given as - y = -2x + 5 Comparing the above line with the…

Q: 3. Show that the lines L1 : x = 2+t, y= 2+3t, z = 3+t and L2:1 = 2+t, y= 3+ 4t, z = 4 + 2t…

A: L1: x =2+t , y= 2+3t , z= 3+t  L2: x =2+t , y= 3+4t , z= 3+t

Q: (a) Find an equation for the line of intersection between the planes x+3y–z= 2 and 2x –y+2z = 5. (b)…

A: Given: Two planes  x+3y-z=2vector a = <1 , 3 , -1 >2x-y+2z=5vector b = <2 , -1 , 2 >

Q: Determine the equation of the plane that contains the lines Li and L2. L: x = 3- t, L2: x = 8 +2 s,…

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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: 12 The lines whose equations are 2x + 3y = 4 and y = mx + 6 will be perpendicular when m is %3D 1)을…

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Q: Find an equation for the line L that contains the point the point P = (−2, 4, 1) and is orthogonal…

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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: Find the point of intersection of the lines x = t, y = -t + 2, z = t + 1, and x 2s + 2, y = s + 3, z…

A: we have to find the point of intersection of the given lines

Q: Consider the line which passes through the point P(1, 3, -5), and which is parallel to the line æ =…

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Q: Find the intersection of the line and plane: 2x + 4y – 3z = 19, r(t) = (-2, 1, –1) +t (1, –1,2)

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Q: Find equations of the lines that pass through the point (0, 4) and are (a) parallel toand (b)…

A: Given,         The equations of the lines that pass through the point 0,4 and the line 5x+2y=3.

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: Show that the lines d1: (7x-15)/ 2 = (7y+34)/ -5 = z/1 and d2: x/1 = (y+1)/-1 = (z+3)/-1 are…

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Q: Find the intersection of the line and plane: 4x + 4y – 3z = 5, r(t) = (1, 1, 1) + t(1, –2, 3) %3D…

A: Given that line and plane are 4x+4y-3z=5  ,rt=1,1,1+t1,-2,3To find :intersection point of line and…

Q: 258. Are the lines of equations and x = −2+2t, y=-6, z = 2 + 6t x= -1 +t, y = 1+t, z=t, t€ R,…

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Q: Find the general equation of the plane perpendicular to the line z – 2 y + 4 1- x = 3 and is 3…

A: We have to find the equation of plane.

Q: The line joining the origin and Pomt of of the linesr (X=1+2t,42-3+4t. y=-5+3t 2 Ction ,zet) and

A: Let the parameter of line L1 is t = t1 and the parameter of line L2 is t = t2. To find the point of…

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: C. Show that the lines with symmetric equations (x y z) and (x+1 are skew, and find the distance…

A: L1 ;  x=y=z     x-01 =y-01=z-01  x1=0    y1=0     z1=0α1=1    β1=1      γ1=1L2:  x+1=y2=z3…

Q: Find the general equation of the plane perpendicular to the line Z – 2 y+ 4 1- x = 3 and is 3…

A: This is a problem of vector algebra and geometry.

Q: 4. Find the equation of the plane that contains the intersecting lines a = 4 +t1, y = 2t1, z =1-3t…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

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: Find the equation of the line containing the point (1, 3, −2) that is parallel to both of the planes…

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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: Find a line equation through the point P(1,2,3) and parallel to the line of intersection of the…

A: Planes as:                       2x+y-z=3x+2y+z=2;   The given point as:                        (1,…

Q: Find an equation of the plane that passes through P(4, 2, – 3) and is perpendicular to the line x+1…

A: Given that the plane is passes through the point (4,2,-3) and perpendicular to line x+1-3=y-12=z2

Q: what is the equation of the plane perpendicular to the intersection line of the x-2y+2z= 3  and…

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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 point of intersection between the two lines: L:x 3t + 1, y = 2t - 1, z = t + 4 and L: 1 x-7…

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Q: . Give an equation of the plane determined by the intersecting lines L1 and L2 = 2t 2+8 L1 : 4 -t…

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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: 1. Determine the point of intersection of the line and the plane if it exists. π: 7x+y+ 5z = 0 x-4…

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

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Q: The equation of line given by the intersection of two planes with equations 3x + 2y – 11z = 30 and…

A: For the above-given equations of plane: <3,2,-11> = 30 = a <13,-12, 52> = -100 = b   a ×…

Q: find the point in which the line meets the plane x = 1 + 2t, y = 1 + 5t, z = 3t; x + y + z = 2

A: Given, The equation of line x = 1 + 2t, y = 1 + 5t, z = 3t and the equation of plane is x + y + z =…

Q: 3) Determine the point(s) of intersection of the lines L₁: (3,1,5) + s(4,-1,2) and L₂: x = 4 + 13t,…

A: Given

Q: Q1/The line joining origin and point of inter section of the lines (x = 1 + 2t, y = -3 + 4t, z %3D =…

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Q: 2x + 3y Find -dA, where R is the parallelogram enclosed by the lines 4x – 4y -- 2x + 3y = 0, 2x + 3y…

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Q: . Find the equation of the line containing the point (1,3, –2) that is parallel to both of the…

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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.