Given the lines L1 and L2: L1: (x,Y.z)=(-4,6,-2)+t(5,4,3), with tER. www L2: (x,V.z)=(7,16,6)+s(6,6,5), with sER. Consider the following statements about L1 and L2: I. The point P=(1,10,1) is a point of intersection of both lines. II. There does not exist a plane containing both straight lines. Of these, with certainty, which are true? a) None b) I AND II c) I d) II

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: Let l,,l2,lz be the lines X(t) = (1,1, 2) + t(1,2,3), X(s)= (9,8,11) + s(2,1,1) and X (r) = (0,0,0)…

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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: 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: Is there a value for k that would make the line between the points (k,2) and (3,8) horizontal? If so…

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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: This first assignment (shaking off the rust) will be a review of some of the basic relationships and…

A: We have to prove that given identity:

Q: Determine the value(s) of k such that the lines 2y= -kx +6 and 3y-x= 2kx+3  are perpindicular.

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Q: Consider lines L, and L,. L4: x = 1 + t, y = t, z = 8 + t, t ER, L2: x – 9 = y – 1 = z - 9 (a)…

A: We have to find whether the lines are parallel or not if they are parallel then find the shortest…

Q: The diagram shows the parallelogram-shaped component that attaches a car's rearview mirror to the…

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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…

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

A: We have to find the perpendicular distance between point Q and line l. Point Q is 1, 0, 1 and line l…

Q: Consider these lines, where s,t, E R 11: [x, y, z] = [2, 1, -4] + t[1, 3, 1] 12: [x, y, z] = [1, k,…

A: Two lines are said to be coplanar if they lies in same plane. The equation of line passing through…

Q: Prove that given lines are skew. L1: [x, y, z] = [1, 3, 7] + t[–1, 1, 2] L2: [x, y, z] = [4, –2,…

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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: Compute yds ds where C is the line segment from (1, 2) to (4, 7).

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Q: (1) What is the relationship between lines 11 and 12? where L:x = 2, y = 1+2t, z = 1+t L2:x = 4 -t,…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

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

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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: Find the point of intersection of the lines r(t) = (1, 0, 0) + t(-7, 3, 0) and s(t) = (0, 1, 1) +…

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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: Find the shortest distance between the skewed lines. l1: = 1+ 2t, y = -1+t, z = 2+ 4t and l2: x= -2+…

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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: If the line joining the two points (5,4)(5,4) and (3,−k)(3,−k) is parallel to the line kx−9y+11=0…

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Q: Let /, be the line described by the Cartesian equations • x= 1 • y-9 = 2(z-5) Let lz be the line…

A: To find the distance between two given lines we need to consider general point on each line. Minimum…

Q: Consider the line L(t)=(5,2t,5t-5) and the point P=(1,5,2). How far is P from the line L?

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Q: Consider lines L, and L,. L4: x = 1 + t, y = t, z = 3 + t, te R, L2: x – 4 = y - 1 = z - 4 (a)…

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Q: If l,, l2, and l3 are nonconcurrent lines, prove that there exist three points. Exactly one each…

A: Three or more points are said Lto be collinear if they all lie on the same straight line If l1 , l2…

Q: Consider a crowded beach where the population of beach-goers is uniformly distributed across its…

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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: Show that the line joining the points P(0,1,2) and Q(3,4,8) is parallel to the line joining the…

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Q: 20. Consider lines €1 and l2. l1 : [x, y] = [1, 4] + [[-7, 2] l2 : [x, y] = [-2, 6] + t[k, 9] a) For…

A: We know that two lines are parallel if their slope are equal and perpendicular if the product of…

Q: 2- The distance d from the point R=(1,4,-3) to the line L: x=2+t,y%3-1-t Z- 3t is 4.43 False True

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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: Construct a line parallel to a given line through a given external point. * R A

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Q: -> For the two lines; ri(t) = [2,4, 3] + t(0,0, 2] and r2 (s) = [5, –1,0] + s[0, –3, 0], the…

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Q: Which of the followings are true? I. L1 : x = 1+t, y = -2+ 3t, z = 4 – t and L2 : x = 2s, y = 3 +s,…

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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: Find the distance between the skew lines i(t) = (3, 0, – 2)t + (7, 9, 0) and p(s) = (4, – 4, – 5)s +…

A: We have to find the distance between skew lines.

Q: Find the length of the line segment described by, (x,y,z)=(1,2,1) +t(-1,5,4)), where 0<t<5.

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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: Compute x2z ds where Cis the line segment from (0,6,-1) to (4,1,5). 7 6 .A O 56 77.B 16/77 .c O 56 3…

A: The line segment is from 4,1,5 to 0,6,-1 . Hence, this line is parallel to the vector, 4,1,5-0,6,-1…

Q: For the two lines; ri(t) = [2,2, 1] + t[0,0, 2] and r2(s) = [15, –1,0] + s[0, –3, 0], the shortest…

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Q: ez ds where C is the line segment from (0, 6,-1) to (4, , 5). Compute

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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: Find the distance from the point (-3,1,0) to the line d(t) = (1, 0, 2)t + (4, – 9, – 2) .

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Q: Suppose that L is a line through the points (a, 2, c) and (3, –4, 2) that is parallel to one of the…

A: Given that: L is a line passing through (a,2,c) and (3, -4, 2) and parallel to one of the axes.

Q: is this true or false......When lines  m  and  n  intersect at point  P  , it follows that   m ∩ n…

A: This is true: in Euclidean geometry/plane. if two lines m,n intersect at a point P ,then m…

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…