Calculate the distance from the point P(9,4,3) to the line which contains points A(1,0,1) and B(2,3,1) using the dot product.

Q: calculate the distance between point(5,2) and the line, 2x+5y=10

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Q: Find the area of the triangle bounded by the lines y=x+3, y=2x-1 and y=-3x+4

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Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: Find the distance between line 1, and the plane parallel to it and containing line I, where 4:…

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Q: Find the distance from the point Q(1, 2, -4) to the plane 2x - 5z = 5.

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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 distance from the point (0, -1, -2) to the plane - 4y – 4z = 5.

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Q: find the distance from the point to the plane. (2, -3, 4), x + 2y + 2z = 13

A: Given:

Q: Find the distance (d) from the point (- 4, 8, 4) to the plane 2x + 5y + 4z = - 50. d =

A: image is attached

Q: I need the answer as soon as possible

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Q: Find the plane that contains the point (0, 1, 2) and the line x = 1- t,y = 2 + t,z = 4 + 3t.

A: Here I am attaching image so that you understand each and every step.

Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y +…

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Q: Find the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10.

A: Given,           The distance between the point 2,-4,3 and the plane 5x-2y+z=10.We know that,…

Q: Find the distance between the parallel planes. x + y + z = 1 and x + y + z = 3

A: The distance between two parallel planes is the shortest distance between their surfaces. Distance…

Q: Find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 + 4t

A: To find the distance between the point Q(3, −1, 4) and the line x = −2 + 3t, y = −2t, and z = 1 +…

Q: Find the distance of the point (2, 2, –5) from the line r(t) = (1+4t, –1+ 4t,7 – 3t) %3D swer:

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Q: find the distance from the point to the plane. (0, 0, 0), 3x + 2y + 6z = 6

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Q: Find the distance from the plane given by 6x − 2y + 3z − 1 = 0 to the point (4, 1, 3).

A: The distance from plane to a point is given by  d=Ax1+By1+Cz1+DA2+B2+C2 Where Plane is Ax+By+Cz+D=0…

Q: Show that the plane 2x − y − 3z = 4 is parallel to the line x = −2 + 2t, y = −1 + 4t, z = 4, and…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

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Q: Find the distance between the parallel planes.2x + y - 2z = 0 and 2x + y - 2z = 5

A: The given parallel planes are 2x+y-2z=0  and  2x+y-2z=5. The objective is to find the distance…

Q: Find the distance from the point (2, 1,−2) to the plane 6(x − 1) + 2(y − 3) + 3(z + 4) = 0

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Q: Find the distance between the line 2x - 3y + z = 6, 2y- z = 4, and the plane passing through the…

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Q: ) Find the distance from the point (4, 1, 2) to the line x = 0, y = 1+ 5t, z = 2+ t.

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Q: find the distance from the point to the plane. (0, 1, 1), 4y + 3z = -12

A: we have to find the distance of the point (0,1,1) from the plane 4y+3z=-12.   as we know that the…

Q: Find the point at which the line 7(t) = (5, – 3, - 6) + t( – 2, - 8, 6) intersects the xz plane.

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Q: Find the distance from the point (4, 1, 2) to the line x = 0, y = 1+ 5t, Z = 2 + t.

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Q: find the distance from the point to the plane. (6, 0, -6), x - y = 4

A: x1,y1z1=6,0,-6…

Q: Find the distance between the point (2, 8, 4) and the plane 2x + y + z = 5.

A: we have to find the distance between the point (2,8,4) and the plane 2x+y+z=5. as we know that the…

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: Find an equation of the plane through (1,8, 5) that is perpendicular to the line x – 2 = 3t, y + 3 =…

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Q: Find the distance between the two straight lines and x=1+1, y=2, z= −1+2+ x=2-t, y=3t4t, z=2t at the…

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Q: Find the distance from the point (1, -4, 4) to the plane −2x−4y+3z=5

A: Given:The point (1, –4,4) and the equation of the plane –2x–4y+3z=5.The distance from the point…

Q: Find the distance from the point (2, 1, 3) to the line x = 2 + 2t, y = 1 + 6t, z = 3

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Q: Find the distance from the point (1, 1, 1) to the plane x + 2y + 3z  = -4

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Q: Find the distance from the point Q(6, -2, 4) to the plane 2x - y + 2z = 4.

A: It is given that a point Q6,-2,4 and equation of the plane 2x-y+2z=4. Here, x1=6, y1=-2, z1=4  and…

Q: -6x - Find dA, where Ris the parallelogram enclosed by the lines -3x+y R – 6x – y = 0, – 6x – y = 2,…

A: I have used jacobian to solve the area of above double integral.thanks

Q: Find the distance from the point (-2, 2, 3) to the plane -3x + y – z = 9.

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Q: find the distance from the point to the plane. (3, 0, 10), 2x + 3y + z = 2

A: the given point is (3,0,10) the given equation of the plane is 2x+3y+z=2 we have to find the…

Q: Find the distance from the point (5, 4, 3) to the plane −4x−1y−1z=4.

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Q: Find the distance from the point A,= (-7,5, 8) to the plane – 5x + 4y+ 3z = -2. Enter the distance

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Q: Find the distance of the point (3,8,2) from the line =22= measured parallel to the plane 3x + 2y- 2z…

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Q: Find the distance between the point (3, -4, 2) and the plane 5x- 2y +z = 10.

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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: standard form of the line with center (5,1) and tangent to the line 7x+2y=17

A: Given Data: Center: (x1, y1) = (5, 1) Tangent: 7x+2y=17   The general equation of tangent is,…

Q: Find the distance from the point (-2, 1, 4) to the plane y = -5

A: Given plane is: y = -5 Given point is: (-2, 1, 4) We know that the distance (d) of a point P(h, j,…

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: find the distance from the point to the plane. (2, 2, 3), 2x + y + 2z = 4

A: We have to find the distance from the point (2,2,3) to the plane 2x+y+2z=4