Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (3,– 1, 7) + r(-5, 2, 1) and the plane 2x + 3y + 4z = 24.

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

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Q: A. Find the angle between the planes x+y+z 1 and x-2y+3z 1, and Find symmetric equations for the…

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Q: find the plane containing the intersecting lines.  L1: x = t, y = 3 - 3t, z = -2 - t; -inf < t…

A: This question is taken from the planes in which we have to find the plane equation. We can write the…

Q: Find the points in which the line x = 1 + 2t, y =-1 - t, z = 3t meets the three coordinate planes.

A: Given line is  x = 1 + 2t, y =-1 - t, z = 3tWhen the line meets xy plane then z=0So, 3t=0Or, t=0

Q: Find the line r that passes through the origin and is perpendicular to the π planes that passes…

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Q: The line : X - 3t, y = 1 - 2t, z = 2 - t is perpendicular to the plane: X - y - z = 1.[g]

A: Given that equation of line x=-3t ,y=1-2t ,z=2-t and equation of plane x-y-z=1To chaque the line and…

Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

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Q: Find the general equation of the plane that contains the point (2,0,3) and the line r = -1+t, y =t,…

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Q: Determine whether the line L : x = 3 – 4t, y= 5+2t, z = 5 + 4t, - is parallel to the plane x - y +…

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Q: Find the equation of the plane that contains the line x=-1+3t, y=5+2t, z=2-t and is perpendicular to…

A: topic - equation of plane

Q: Find the point at which the line x=1+t, y=3-2t, z=1-t intersects the plane 2x+3y+3z=0

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Q: Find the point P where the line x = 1 +  t,  y  =  2t,  z = - 3t  intersects the plane x + y - z =…

A: Given line: x=1+t,  y=2t,  z=- 3t

Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z 3 -12…

A: The point of intersection will satisfy the line as well as the Planes equation.

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: Find the point at which the line intersects the given plane. x = 2 − 2t,    y = 3t,    z = 1 + t;…

A: Given that  x = 2 − 2t,    y = 3t,    z = 1 + t;    x + 2y − z = 4 first we will substitute values…

Q: Let L be a line which passes through the point (-5, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Find the plane containing the intersecting lines L1: x = -1+t, y= 2+t, z = 1 – t; L2: x = 1 – 4s,…

A: The given intersecting lines are  L1: x=-1+t,y=2+t,z=1-t; -∞<t<∞L2: x=1-4s,y=1+2s,z=2-2s;…

Q: Determine the way in which the line [x, y, z] = [2,−3, 0] + k[−1,3,−1] intersects the plane[x, y, z]…

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Q: (A) Find the Distance between the point (x.y.z) and the plane 3x+2y+6z = 6 If the plane meet with…

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Q: Find the point of intersection of the line l: x = 2+ 3t, y = 1 – 6t, z = 4 – 2t with the plane - 2x…

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Q: Find the equation of the plane that contains point P1(1,0,3) and orthogonal to line L1:(5t – 1,3 –…

A: Consider the line L1given by the vector form: L1:5t-1, 3-2t, t    :-1+5t, 3-2t, 0+t    :-1, 3, 0+5t,…

Q: 10) Find the point of intersection of the lines L4:x = 1+ 2t, y = 2 + 3t, z = 3 + 4t and L2: x = 2 +…

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Q: .) Find the plane which contains both lines: a. x = 1-4t, y = 1+2t, z = 2-2t b. x = -1+s, y = 2+s, z…

A: Since you posted here 3 questions,  I can answer only first one.  Please reupload remaining two…

Q: Determine whether the plane x + y + z = 9 and the line x = t, y = -2t + 1, z = t + 2 are parallel,…

A: The given equation of line is in parametric form, x=ty=-2tz=t+2 Convert it into the cartesian form,…

Q: Consider the line which passes through the point P(5, 2, -1), and which is parallel to the line x =…

A: Introduction: In three dimensional geometry, there are three fundamental planes referred to as the…

Q: Find the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y -…

A: We have to find the point at which the line intersects the given plane.

Q: Find the distance between two lines (L1: x=3t-1, y=t+6, z=2t+3 and L2: x=2t+6, y=2t+11, z=-t+3)…

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Q: 1. Determine the point of intersection between the line, L: x = 3+t, y=4-5t, z=1-7t, te R, and the…

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Find an equation for the line of intersection of the planes bx+z=0, by+ cz =b, where b,c are real…

A: the equation of the line of intersection pf the given planes ...

Q: Find the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y –…

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Q: If the line x=1+(a+2)t, y=1-bt, z=-1+(c-1)t and the plane -x+2y-323D0 are orthogonal to each other.…

A: Given: Ratio of lineA^=<a+2,-b,+c-1> Ratio of planeB^=<-1,2,-3>

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

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Q: Determine the point of intersection of the line and the plane. e:[x, y, z]= [3, 1, 2]+t[1, -4, -8]…

A: Finding the general point in the line substituting in the equation of a plane

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: b) Find the equation of the plane containing lines ₁ : x = 2+5t, y = 4+2t, z = -t and l₂: x=2-t₁y =…

A: We have to find the equation of the plane containing lines l1 : x=2+5t, y=4+2t, z=-t and l2 : x=2-t,…

Q: Consider the lines x – 4 l2 : 4 - 1 l1: x= 4 – 3t, y = 2t, z = 1 + 5t , %3D 2 (b) Find an equation…

A: Given that:                        Two lines are: l1: x=4-3t, y=2t, z=1+5t,  l2:x-44=y1=z-12

Q: Determine the point of intersection, if such a point exists, for the line €: (x, y, z) = (-1,-6, 5)…

A: Given: Equation of line as, l:(x,y,z)=(-1,-6,5)+n(1,3,-2) And the equation of the plane is given as…

Q: Find the point of intersection of the line x = 2 − 3t y = 4 + 2t −∞ < t < ∞, z = 3 − 5t, and…

A: x=2-3ty=4+2tz=3-5tand the plane 2x+3y+4z+8=0

Q: Find the cartesian equation of the plane determined by the two intersecting lines x-4 y+1 z-2 L1: 3…

A: Here,  v1=3i+2j+kv2=5i+3j+2k v1×v2=ijk321532=i4-3-j6-5+k9-10=i-j-k Thus, the equation of the plane…

Q: If the line x=1+(a+2)t, y=1-bt, z=-1+(c-1)t and the plane -x+2y-3z=0 are orthogonal to each other.…

A: The parametric equation of the given line is  x=1+a+2ty=1-btz=-1+c-1t The general form of the…

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: Check that the line (1,0,1)+t(3,0,1) is parallel to the plane -2x+4y+3z=13 and calculate the…

A: For the equation of the plane , the direction vector of the normal to the plane is given by . For…

Q: Determine the way in which the line [x, y, z] = [2, −3, 0] + k[−1, 3, −1] intersects the plane [x,…

A: Here given as x, y, z=2, -3, 0+k-1, 3, -1⇒x=2-k⇒y=-3+3k⇒z=-k .......1 Thus the equation of the line,…

Q: Find the point at which the line intersects the given plane. x = 3 - 3t, y = 4t, z = 1 + t; x + 2y -…

A: Given line ,x=3-3ty=4tz=1+t   -1and plane , x+2y-z=6

Q: Find the point at which the line intersects the given plane. x = 4 - t, y = 5 + t, z = 3t; x - y +…

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Q: Find the point of intersection of the lines x = 2t + 1, y = 3t + 2, z = 4t + 3, and x = s + 2, y =…

A: Equate the x and y coordinates in t and s domain to obtain values for t and s.

Q: Does the line r(t) = intersect the plane 5x - 2y - z = 21 and if so, where?

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