Q2: 1) Find the equation of the Line (L1) that pass through the point (0,-3, 8) and parallel to the Line (L2) given by x = 10 + 3t, y = 12t and z = -3 – t. 2) Find the coordinates of the point where the line will pass through the xz-plane

Q: What is the equation of the line that is paralel to y-3r+ 12. passing through (4, 2), witten in…

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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: Find the point(s) on x=3-y² that are closest the point A=(1,0)

A: Our Aim is to find the points on x=3-y2 that are closest the point A=(1,0).

Q: 10) Find the equation of the line of the intersection of the planes 2x+3y+7z+2=D0, x+2y-3z+5=D0.

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Q: Find the point on the plane x − 2y + 3z = 6 that is closest to the point (4,2,0).

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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: Q1 Frad Pavametric equations for the line through the Point (o,t, 2) that is Perfandicutar to U…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: #4 Find y! of 3-y3+y2+5y-x²=D0.use it to find the eguation of the line that is perpendicular to the…

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Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

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Q: 3+i 1. Evaluate I- (2Z43) dz 1-2i Aus 17+191 a, directly to, along the path x=26+1g Y= 4t-t-2 C.…

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

Q: The distance from a point P1(x1, Y1) to the line ax + by +c = 0 is laxi + by, + c] Va? + b2 Use this…

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Q: Find an equation for the plane through P0(-3, 0, 7) perpendicular to n = 5i + 2j - k.

A: given that the plane passes through (-3,0,7) perpendicular to n=5i+2j-k. we need to find the…

Q: Find the equation of the line in standard form (i.e., y = mx + b) that conatins the point (-3,5) and…

A: We have to find the equation of line in standard form if it is passing through the point -3, 5 and…

Q: What is an equation of the line that passes through the point (–6, –6) and is paralle to the line x…

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Q: Q5: Find the distance of the point (2. –2,1) from the line х-2 y-3 = z+2 2 4 3 measured parallel to…

A: we have to find the distance of the point (2,-2,1) from the line x-22=y-34=z+23 measured parallel to…

Q: The plane containing the point (2,5,0) and parallel to the plane 3x – 7y + 6z = 8 has equation Ах +…

A: Recall:      The equation of the plane parallel to Ax+By+Cz=D and passes through the point  α,β,γ ,…

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: The equation of the line tangent to the intersection of two surfaces 2 = a2 and z 25- y? at the…

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Q: Find the acute angles between the intersecting lines x = 2 + t, y = 4t + 2, z = 1 + t and x = 3t -…

A: Given: The equation of lines x = 2 + t,  y = 4t + 2,    z = 1 + t      and x = 3t - 2,   y = -2,   z…

Q: Q5: Find the distance of the point (2. –2,1) from the line x-2 y-3 z+2 %D 2 4 3 measured parallel to…

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Q: Find the veeton equation of a Line L going thagh the P= C-6,2) $ paeallel to the ine point %3D…

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Q: :) Find the shortest distance from the point P(3, 1, 1) to the plane with equation 2x – 3y + 2z = 22…

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Q: Find the point on the plane 4x+5y+x=11 that is nearest to (2,0,1). What are the values for x, y, and…

A: The equation of the plane is

Q: Find equation of Plane teter mined by the Lines Li. X = t-29 y = 2t+3 Z= +4 and Lz! X…

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Q: 8) Determine if the line given by r(t) = intersects the xz-plane. If so, determine at what point.

A: we have to find the point of intersection.

Q: The coordinates of a point on the line x+ y+1 = 0 which is at a distance /2 units from the line 3x +…

A: Given: The line x+y+1=0 which is at a distance 2 units from the line 3x+4y-2=0 To find: Coordinates…

Q: 1. Find an equation for the plane through Po (0,2,-1) perpendicular to n = 3i - 2 j- k ?

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A: Definition used-   To keep the temperature constant, the insect has to move in a direction that is…

Q: How do you compute |PQ| from the coordinates of the points P and Q?

A: Suppose the coordinates of P and Q  are given as, a,b and c,d. Then to compute PQ⇀,   PQ⇀=c-a2+d-b2…

Q: Find the equation of the curve, in the XY plane, that passes through the point (2, 2) and is such…

A: Differential equation

Q: The distance from a point P₁(x1, y₁) to the line ax + by + c = 0 is lax₁ + by₁ + cl √² + b² Use this…

A: SOLUTION-

Q: 6) = Find the point at which the line intersects the given plane. x =3 - t, y = 2 + t, z = 5t; x - y…

A: Equation of a Line in Parametric Form: where are functions of and is the parameter The equation of…

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A: As a first step we need to find the gradient of the surface and evaluate the same for the point (1,…

Q: Find an equation for the set of points equidistant from the y-axis and the plane z = 6.

A: we  have to find an  equation for the set of points equidistant from the y-axis and the plane z =…

Q: find the equation of the line through (0,2,1) that is perpendicular to both u= 4i + 3j − 5k and the…

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Q: 2. Find the equation of the line that is parallel to the intersection of planes 12, 2x-8y + z = 0…

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Q: Suppose a particle P in R' is traveling upward in a straight line which is perpendicular to the…

A: Given: Suppose a particle P in R3 is traveling upward in a straight line which is perpendicular to…

Q: 3. Find the shortest distance from the origin to the plane x – 2y – 2z = 3. |-

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

Q: 1. Find the Cartesian equation of the curve represented by x = 4t + 3 and y 16t - 9, -0 <t<o.

A: Try to eliminate 't' to establish relation between x and y.

Q: [x=t+1 B- Find an equation plane pass through point (1,0,0). If the line L₁ y=-2t Z -3t…

A: Given: 1,0,0 x=t+! y=-2t z=-3t

Q: The line 2x + 5y = 1 meets the curve x² + 5xy - 4y² + 10 = 0 at the points A and B. Find the…

A: The midpoint of the line joining the points: x1, y1 and x2, y2 is x1+x22, y1+y22. The roots of the…

Q: point

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Q: ind the equation of a line tangent to the circle x2 + y2 - 8x -14y + 52 = 0 at point (7,5) a.…

A: we have the equation of circle is  x2+y2-8x-14y+52=0  .........(1) differentiate with respect to x

Q: Find the point (Xo, Yo) on the line 4x + 6y = 12 that is closest to the origin. (Xo, Yo) =

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Q: 4 Find a. the equations of the tangents to the circle x +y +4x-2y – 24 = 0 at the points where the…

A: Given,  (a) Equation of the circle   x2+y2+4x-2y-24 = 0  We have to find the equations of tangents…

Q: Q1. Find the equation of the plane determined by the lines : L₁: (x = -2+1, y = 21 +3₁ Z=4-1), L₂:…

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Q: (i) Find the distance from the point P(-1, 2, 1) to the plane II1 : 2x + y – 3z= 4. (ii) Find an…

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Q: Q7) Find the equation of the set of points located three units away from the plane - 2х + бу + 3z…

A: