Find the distance from the point (-6,-2,0) to the line a(t) = ( – 1, – 2, – 5)t + (3, – 6, 6)

Q: find the distance d between the points P1 and P2. P1 = ( - 0.2, 0.3); P2 = (2.3, 1.1)

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Q: Find the abscissa of the point on the graph of y=V 2x – 1 that is parallel to the line 2x - y+1=0

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Q: Find the point (x0, y0) on the line 4x + 9y = 12 that is closest tothe origin.

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Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: H

Q: 15. Find the point on the line y 3x that is closest to the point (50,0).

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Q: Find the line L, that passes through the point P(1,2) and parallel to the line L2: x+2y=3.

A: Given data is: The equation of the line L2: x+2y=3 To find the equation of the line L1 that passes…

Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: Ex: Find the distance between the pt G(4₁-4,4) and the line x=2t₁ y=Z-3, z = at +2₂

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Q: Find y as a function of t if 3y′′+31y=0 y(0)=7, y′(0)=3

A: Find y as a function of t if 3y′′+31y=0 y(0)=7, y′(0)=3

Q: Find the distance between the points (3,6) and the line x - 2y +3 =0.

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Q: Find the distance between the point (0, 4, -1) and the line defined by r(t) = +t

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Q: Find the distance d between the point M(5, 2, 4) and the line x- 8 y -2 Z-2 %D -8 -9 7.

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Q: Q4) Compute f z'dz, where C is the path formed by the line segment from -3 to 3 and the semicircle…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: The temperature of a rectangular plate bounded by the lines x = ±1, y = ±1, is given by T = 2x2 −…

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Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: B. Find the distance between the point (1. 1.3) and the line =z-3) OMI NOTL

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Q: Find the shortest distance, d, from the point (4, 0, –4) to the plane x + y + z = 4.

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Q: nded by the curve y2=4x and the lines x = 1 and x = 4.

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Q: Find the livus of points that are equidistant to the point F(0,2) and the line y=-2

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Q: Find y as a function of t if 5y′′+31y=0 y(0)=4,y′(0)=7y(t)=

A: The given differential equation is  5y''+31y=0   ......(1) and the initial condition is y(0)=4 and…

Q: T Find the tangeut line to the curve 1 2rg+ 12 at the point (2. 1).

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Q: Find y as a function of t if 8y′′+32y=0 y(0)=9, y′(0)=6.

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Q: Find the shortest distance, d, from the point (5, 0, -8) to the plane x + y + z = 8. d =

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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 points on the line 3x – 4y – 1 = 0 which are at a distance of 5 units from the point (3,…

A: Solving the problem by finding the points.

Q: Find a relationship between x and y such that (x, y) is equidistant the same distance from the two…

A: Given points are: 4,-1 and -2,3 The distance between the points 4,-1 and x,y is: d1=x-42+y+12 The…

Q: Find y as a function of t if y(0) = 7, (0) = 6. y(t) = = 49y" + 140y + 136y = 0,

A: The given DE is: 49y''+140y'+136y=0 So, the auxiliary equation of it is:…

Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: Find the point at which the line f(r) = -z+1intersects the line g(z) = 4x +1 %3D

A: At point of intersection both the functions will have the same value therefore f = g

Q: Find the area of the triangle that lies in the first quadrant (with its base on the x-axis) and that…

A: y=2x-4 and y=-4x+20 We need to find the area of the triangle that lies in the first quadrant (with…

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y=-2t z = 2t

A: Write the vector of the given line using x=4t, y=-2t, and z=2t. L→=xi→+yj→+zk→   =4ti→+-2tj→+2tk→…

Q: Q6) Find the distance from the point S= (1, 2, 1) to the line x = 2 -t, y=-1 + 2t, and z= 2 + 2t.

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Q: Find the point on the x-axis that is equidistant from the points (0,−1) and (5,−3)

A: To find the coordinates of the point satisfying the given conditions

Q: At how many points do the curves r₁ (t) = ((t+1)², -t2- 2t, t+2) and r₂ (t) = (1 − t², t, t)…

A: This is the problem of parametric equations and the theory of curves.

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: to Find the mid Point. M.of the line Segment Joiningthe points. S:(-8,2)) and'f =(0i6)

A: Basic algebra problem

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: The area (in square units) between the curve defined by y = x³, the x-axis, and the lines x = -1 and…

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Q: Find y as a function of t if 7y" + 32y = 0, y(0) = 2, y'(0) = 4.

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Q: Q2) find the distance between two lines L1: x= 1 +4t, y=5 - 4t, z=-1+5t L2: x=2 + 8t, y=4 - 3t, z-5…

A: Method 1:

Q: The area bounded by the curve y = 4x and the lines r = 6 ,x = 12 and a – axis is 144 square units O…

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Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Equidistant points mean that the distance of two points represented by P1 and P2 is equal to the…

Q: Find a distance from the point S(1,1,5) to the line x=1+t, y=3-t,and z= 2t

A: We need to find the distance of the point (1,1,5) and the given line.

Q: Find the slope for f(x,y) = xeyat P (2,0) in the direction of the line from M(2,0) to N(-1,2)

A: We have to find slope

Q: Find y as a function of t if 9y" + 12y' = 0, y(0) = 3, y'(0) = 3. y = 3e^(-4/3t)+3

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Q: B. Find the point on the line y = 10 – 2x that is closest to the origin. REFLECTION

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Q: 11. Find the distance between the point (1,0,-1) and the line x = 5 – t, y = 3 t, z = 1 + 2 t.

A: 11) The direction ratio of the lines  = -1,3,2 The direction ration of the point (1,0,-1) and the…

Q: 5. Find the distance between the point (4, 3, 1) and the line f(t) = (2x - 1, –3y + 1, 2)

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Q: Q2: Find the distance from the point R( 2,2,10) to the line: x=t y=1+t z = 3-t

A: Here first we select a general point on the line Now, we find the direction vector of that point to…