Find the intersection of the line r(t) = (1,0 t(4, 12, 2) and the plane x – z = b. (Give your answer in the form (*,*,*). Express numbers in exact form. Use symbolic notation and fractions where needed.) intersection point:

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: Find a plane containing the point (7,3,5) and the line x(t) - 3 + t | y(t) 8 +t z(t) - 3 + 5t

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Q: 2.) Find the Symmetric form of the equation of the line of in tersection of the two Planes X-Y +Z…

A: Let a, b and c be the direction ratios of the required line. Since the required line lies in both…

Q: Let L be a line which passes through the point (-7,0,1) and is perpendicular to the plane x + 2y +…

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Q: Find the point on the plane x+5y+2z=14 closest to the point​ (1,1,1).

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Q: The distance from (9,-6, 7) to yZ-plane is A9 O B. 6 OC. 166 OD. 85 O E.7

A: Distance of a point (a,b,c) from yz plane is as In yz plane x coordinate is zero and y= b and z= c.…

Q: Find the intersection of the plane: x - z = 6, and the line r(t) = (1,0, -,1) + t(4,9,2)

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Q: Write a paragraph explaining how the distance formula giving the distance between two points (x1,…

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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 distance between the plane P:8x+3y+9%= 0 and the point (1,-5,20)

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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 distance from (2, -7, 8) to each of the following. (a) the xy-plane (b) the yz-plane (c)…

A: Here we find the distance from 2,-7,-8 to a xy plane b the yzplane , c the xz plane d the x-axis e…

Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: EX Find the reglon in the z-plane represented bye

A: Given

Q: Find the distance (d) from the point (– 6, – 8, – 7) to the plane 5x – 2y + 2z = 25. - d =

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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: 3. Find the point in which the line x=+3t , y=1- 2t , and z=1+3t meets the plane x+y-z=1.

A: Here, given equation of line is,   And the given equation of plane is, From (1) and (2),

Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: To find the distance from the point 0,1,1 to the line of intersection of the planes:…

Q: Find a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

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Q: Find the point on the plane x+y+z=-46 that is closest to the point (1,1,1).

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Q: Indicate on an xy-plane those points (x, y) for which the statement holds. |x − 3| ≤ 5 and |y + 2|…

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Q: If 1x, y2 are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

A: If (x,y) are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

Q: A(n)________ is the collection of points in the plane the difference of whose distances from two…

A: The given statement is "A(n)________ is the collection of points in the plane the difference of…

Q: Verify Green's theorem in the plane for M = -2y and N = x , where C is the semi circle x2 + y? = 9,…

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Q: Find an equation of the plane containing the point (1,2,-2), and the line: x= 2t, y= 3-t, and z…

A: To find the equation of plane we need to find its normal vector. To find the normal vector, we…

Q: Find a plane containing the point (-3,3,-3) and the line F(t) = +t

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Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: Use equation of plane

Q: Find the point on the plane x+ 2y - z 12 that is nearest the origin.

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Q: Let L be the line that passes through the point  (1,3,1 ) and orthogonal to the plane 3x-2y + 5z =…

A: In the question we have to find interacting points at which line and plane intersect.

Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Find the point at which the line (4, –1, 4) + t(4, 2, 3) intersects the plane 4x 5y + z = 88.

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Q: 2. Use analytic geometry to verify that quadrilateral JKLM is a parallelogran 1C). YA K(-1,1) 2 -2 0…

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Q: 5) Find the distances by drawing the figures and right triangle used to calculate a. Between 1₁ =…

A: Given: Let's determine the distance for the following, a) medium of l1=2+2t,-1+t,-3t and…

Q: Find the distance from (2, -2, 9) to each of the following. (a) the xy-plane (b) the yz-plane (c)…

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

Q: Find the point in which the line through the (3,-1,2) perpendicular to the plane x +2y -5 z = 4…

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Q: The distance from the point P(2, 1, 0) to the plane 2x + y + 2z+ 6 = 0 is 3.7 True O False

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Q: Find the number  a such that the line x = a  bisects thearea under the curve  y = 1 / x 2  , 1<…

A: Our Aim is to find a number such that line x=a bisects the area under the curve y=1x2, 1≤x≤4.

Q: Find the point in which the line through P(3, 2, 1) normal to the plane 2x - y + 2z =-2 meets the…

A: Direction ratios of normal to plane 2x - y + 2z =-2  are <2,-1,2>, since line is normal to…

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

A:

Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane x + 2y +…

A: Here we find the equation of line L and also find the intersecting point of line and plane.

Q: х —7 у-5 z-1 L: 4 -,P: 2x + y – 7z +1 = 0 6. 3

A: Given Data: Line: x-74=y-53=z-16 Plane: 2x+y-7z+1=0 Let t is a constant variable for line,…

Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

A: The line L is perpendicular to the plane, x+2y+4z = 0 Hence the direction ratios of the line L is…

Q: Find the distance from the point of intersection of liies ( X=t, y=3-3t, =-224) and (x=1+t y=4rt,…

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Q: Let L be a line which passes through the point (-3, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Find the points on the plane r - y = 2 – z closest to the point (1, 1, 1).

A: We will find the closest point on the given plane as following.

Q: Find the equation of a plane containing Po (1, 2, 3) and perpendicular to n = .

A: We have to find the equation of a plane containing P0 (1,2,3) and perpendicular to n = <1, -1,…

Q: -:Q1 Evaluate , (x- 2y) dA, where R is the parallelogram in the xy-plane with vertices (0,0), (4,1),…

A: The objective is to evaluate ∫∫Rx-2ydA where R is the parallelogram in the xy plane with vertices…

Q: Find the point on the plane x – 3 y – 2 z = 14 that is closest to the point (0, 3, 3) .

A: We have the plane x-3y-2z=14 The normal vector to a plane ax+by+cz=d is a,b,c Hence, the normal…

Q: Given F(x.y.z) (x+y+Zi +(x-yj+(xz-2)k what is CurlF at the point (1,-1,3)? You should write your…

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