Let the point A = (-1,3,-3 ) be the lines r:X=(1,1,-2)+t(2,-1,2) te R a) The distance between the line r and the point A

Q: Verify that the two lines are parallel and find the distance between the lines. L1:   x = 2 − t,   y…

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Q: Find a plane containing the point (6,-7,7) and the line x(t) y(t) z(t) = = = - 2 - 6t - 1 + 5t 5-t

A: Here we have to find the equation of plane

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: 04: Find the distance between the parllel lines L, and L2 where L1: x = 2 - t, y = 2t, z = 1+t L2: x…

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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: 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: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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Q: Find the distance between the point (-3, 1, 5) and the line given by x = 5+t, y = 1- 2t, and z = 3-…

A: Given : Point A ( -3,1,5) x = 5+t  y=1-2t  z=3-t

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

A: Equation of the line :       x-x0a = y-y0b = z-z0c=k ; where x0,y0,z0 is a point and a,b,c is the…

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

A: Answer

Q: Let l be the line given parametrically by x = (1, 3) + t(-2, 1), tЄR. Which of the following points…

A: A parametric equation is an equation that employs an independent variable  to define the dependent…

Q: A) Find the distance from the point (1,1,1) to the line = =

A: the solution is given by the image attached  and since it is the square of distance which we have…

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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Q: consider as straight r1: (x, y, z) = (1,1,1) + t (1,2,3), t∈R r2: (x, y, z) = (1.1, −2) + s (1.2,…

A: Equation of line:  r: (x, y, z) = (x1, y1, z1) + t(a, b, c) The line r, passes through the point…

Q: Construct a line perpendicular to the line given through the point P at the right.

A: To plot the line perpendicular to the given line through the point P

Q: d s: X = (0,1, -1) + λ (1, α, 2α) are coplanar, in which case study its relative position.

A: Consider the given lines. r: X=(1,0,2)+λ (2, 1, 3) And, s:X=(0,1, -1)+λ(1, α, 2α) Let r and s are…

Q: Let A be the point with coordinates (-3, 2, -1) and let B be the point with coordinates (2, 0, 0).…

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

A: The direction vector of the line  given by:        x=1+4ty=2+1tz=3+3t is :    r→=123+t413 So, The…

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. %3D

A: Given line is                                                       l:1, -1, 1+t0, 2, 1 vector…

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 distance between the point (−3, 5, 1) and the line given by x = 1 + t, y = 5 − 2t, and z =…

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Q: Consider the points P(2, −1, 0), Q(5, 0, 0), and R(3, 1,√5). Find the coordinates of the point S on…

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Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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Q: Find the distance between the point (-1, 5, 3) and the line given by x = 5 + t, y = 1 - 2t, and z =…

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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 the distance from the point P(2,1) to the line v = x + 2

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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: Let A be the point with coordinates (-2, -1, -1) and let B be the point with coordinates (2, 0, 0).…

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Q: Find the relationship between x and y such that point (x,y) is equidistant from the points (7,1) and…

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Q: Consider the line which passes through the point P(2 -3, -4), and which is parallel to the line x =…

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Q: Find the point ( x, y) such that (1, 3) is the midpoint of the line segment connecting а. (х, у) and…

A: NOTE-Since you have posted a question with multiple sub-parts, we will solve first three subparts…

Q: Consider the line which passes through the point P(-2, 4, 3), and which is parallel to the line x =…

A: Consider a line  L1:x=1+7t,y=2+7t,z=3+4t Point : −2,4,3

Q: Verify that the lines are parallel, and find the distance between them. (Round your answer to three…

A: To find if the two lines are parallel using their normal vectors and finding the distance between…

Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

A: Given two lines, x=2-t, y=3+3t, z=4+3tAnd x=5t, y=1-15t, z=4-15tThat isx-2-1=y-33=z-43=t…

Q: Find the relation between x and y such that the point (x,y) is equidistant from the points (7,1) and…

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Q: Verify that the two lines are parallel, and find the distance between the lines. (Round your answer…

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

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Q: Let lį be the line described by the Cartesian equations • x =1 • y-4 = 2(z-6) Let l2 be the line…

A: Given that l1 be the line describe by the cartesian equations                   x=1y-4=2(z-6) and…

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: 4. Determine the intersection of lines:L,:= = and Lz X=Y-1=2 11 >\J

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Q: Let A be the point with coordinates (0, -3, 3) and let B be the point with coordinates (2, 0, 0).…

A: Given: A=0,-3,3B=2,0,0

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: Consider the points P(1,0,3) and Q(5, 2, -1), and the line 1: { x = -7-2t y=t z = 9+t

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.