2. Given three points A(1,-1,-1), B(-2,2,1), and C(0,1,-2). Determine: a. Equation of the line through A and B in vector and coordinate form. b. Equation of the line through A and C in vector and coordinate form. c. Equation of the line through B and C in vector and coordinate form.

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: 16. Determine which line is parallel to the line with Cartesian equation 2x + 3y + 5 = 0. a. 7 =…

A: (16)given equation 2x+3y+5=0 claim- determine which line is parallel to the line with cartesian…

Q: Find the equation of the line that passes through the point (-1, 3) and is parallel to the line 5x –…

A: Two parallel lines have the same slope.   The slope-intercept form of a line is given by:…

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: Let lines L and L2. L: (t) = (1,5, -2) + (1, -2, 1)t L2: F2(t) = (0, -2,-2)t + (2, 5, 1) %3D 1.…

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Q: we consider the equations of a line in symmetricform, when a = 0, b = 0, c = 0.x − x0/a = y − y0/b =…

A: Given, Point P0(-2,3,3) with direction vector, v=(2,4,3)

Q: Find the value of m so that the line passing through (-m,-1,2) and (0,2,4) be perpendicular to the…

A: The correct answer to this question is m=1 or m=2.  But they don't match with any of the given…

Q: Find the symmetric form of the equation of a line that passes through the points 4 = (2,4,-3) and B…

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Q: Find the equation of the line through point (2, 1/2, -3) and is perpendicular to the plane -x+4y+3z…

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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: Determine whether the lines h and I, intersect, are parallel, or are skew. 1: n= 4i+3j+ (i-j+6k) 12:…

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Q: Ux the fact that х у 1 a b 1-0 a b 1 to deiermine the equation of the line passing through the…

A: Let (x,y) be a point on the line connecting the points Now if  they are on the same line, the area…

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: Give an example of a pair of perpendicular lines, neither of which is parallel to the coordinate…

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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: In Cartesian space, the point form of a line is e: (x, y, 2) = (2 + r, -3 + 2r, 5 5r). a) Find the…

A: In cartesian space, the point form of a line is  l : (x, y, z) = (2+r, -3+2r, 5-5r).   a) Find the…

Q: Find the equation of the line perpendicular to through (7, 2) through (-1,7/2) through (1/3, 13)…

A: The line perpendicular toa) 2y-3x=1 through 7,2b) 9x+15y+6=0 through -1,72c) x+y=1 through 13,13…

Q: If the line through the point (3.-4,-1) and parallel to the vector i+j+k. The equation of the line…

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Q: Find the equation of the line that is perpendicular to x – 3y = 6 and passes through the point (2,…

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Q: Write an equation of the line containing the given point and parallel to the given line.  Express in…

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Q: Find equations of the lines that pass through the given point and are (a) parallel to and (b)…

A: We have to find the equation which is parallel to x-y=4 and passes through the point 2.5,6.8. Also…

Q: Let I, be the line described by the Cartesian equations • x= 1 • y-9 = 2(z-7) Let l, be the line…

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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 equations of the lines that pass through the given point and are (a) parallel to and (b)…

A: A function is usually represented as f(x) where x is the input to the function and f(x) represents…

Q: Determine whether the lines k = 2x - 1 and w 2x + 4 are parallel, perpendicular, or %3D %3D neither.

A: The given diagram has 4 sides equal in length A parallelogram with all sides equal is called as a…

Q: Let L7 be the line passing through the points Q1=(-5, -5,-3) and Q2=(-1,-3, 3) and let L2 be the…

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Q: 30. The slope of line / in the standard (x, y) plane is . Which of the following is an equation of a…

A: Givenslope of line l=m1=23To calculate: which line is perpendicular to line l.concept: Two lines are…

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: For the line that contains the points P(-1, 2, 4) and P2(3, 4, 7), find a) a direction vector. b) an…

A: The line contains the points P1-1, 2, 4  and  P23, 4, 7. a). Direction vector is, P1P2→=3--1, 4-2,…

Q: Show that if a, b≠0, then the line with x-intercept x = a and y-intercept y = b has equation…

A: Given: x-intercept=ay-intercept=ba, b≠0 To Find:  To show the equation of the given line isxa+yb=1

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: Determine whether the lines (1,1,1)+ t(1,2,-1), and (3,2,1)+(-1,-5,3) are parallel, intersect, or…

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Q: Which of the lines x – y + 3 = 0 and x – 4y –7= 0 is father from the origin? -

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Determine whether the lines given by the symmetric equations x - 1 y - 2 z - 3 %3D 2 3 4 and x +1 y…

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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: If a line segment has endpoints A(2x + 7,4y) and B(4x + 3,- 2y), what are the coordinates of the…

A: A line segment has endpoints A2x+7, 4y and B4x+3, -2y

Q: For the line €: (x, y, z) = (5, - 3, 2) + n(1, 2, - 2), find a) a point of the line. b) a direction…

A: Given parametric equation of line - x, y, z = 5,-3, 2+n1, 2,-2x, y, z = 5,-3, 2+1n, 2n,-2nx, y, z =…

Q: Determine the intercepts of each plane. a) [x, y, z] = [1, 8, 6] + s[1, –12, –12] + t[2, 4, -3]

A: As per policy, only the first question is answered as you have asked multiple questions asked in a…

Q: Find the general forms of the equations of the lines that pass through the point (2, −1) and are…

A: Line passing through the point (2, −1) and is parallel to the line First we find the slope of the…

Q: For the line €: (x, y, z) = (2, 3, 4) + n(3, - 2, 5), find a) a point of the line. b) a direction…

A: the given line is: l:x,y,z=2,3,4+n3,-2,5 we have to find: (a) a point of the line. (b) a direction…

Q: II. Fill in the missing entry in each row: Equation of line m Point P Point (P) X = 0 (x,y) 1.) Y =…

A: II) 1, Given line equation, X=0 Image of P(x,y) w.r.t line X=0 : line equation ⊥to X=0: Y=C Let…

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: Show that the following sets of points are collinear and find the equation of line…

A: Three or more points are collinear, if slope of any two pairs of points is same. With three points…

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: Example 4: Decide whether the following lines are perpendicular? Line j 3x +5y = -15 Line k 6y - 10x…

A: We have to determine if the following lines are perpendicular or not. Line j : 3x + 5y = -15 Line k:…

Q: Write an equation for the line through the point (1,3) parallel to the line y = x + 10. Oy=z O y =…

A: Given query is to find the Indicated line.

Q: Determine whether or not the line through the points A(0, –4, 2) and B(5, –1, 0) is perpendicular to…

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