8) Find the distance from the point S(0,0,0) to the line through(-1,-1,2) parallel tov = 31 + k.

Q: Compute ye*ds where Cis the line segment from (1,2) to (4,7). .A 16 34 e4

A: According to the given information, it is required to calculate the value of integral.

Q: 6. Find the shortest distance from B6,0,0) to the pane Ax + By tCz +D= 0 where A, B,C and D SR .

A:

Q: Let I be the line (1, -1, 1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l. distance

A:

Q: Evaluate the line integral 6ydx + 4xdy where C is the straight line path from (2, 3) to (5, 5). Jc…

A:

Q: A________ is the set of points P in the plane such that the ratio of the distance from a fixed point…

A: The conic section is known as the set of points, in which the curve of any of the conic, that are,…

Q: Evaluate (x+ y)ds where C is the straight-line segment x = t, y= (4- t), z=0 from (0,4,0) to…

A: Given that x=t,y=4-t,z=0 from (0,4,0) to (4,0,0) evaluate ∫cx+yds

Q: Determine the value(s) of k such that the lines 2y= -kx +6 and 3y-x= 2kx+3 are parrallel.

A:

Q: Compute Sc(2x + V) ds, where C is the curve from (0,0) to (2, 4) along y

A: Given

Q: #3 Find the line equation(s) of the line(s) through point P(1, 0, 1) that meets the following line…

A: Given :  Given:P(1,0,1)L: x,y,x=1,2,0+t2,-1,2P0=1,2,0Aim: To find a line(s) through point P,…

Q: Compute yds ds where C is the line segment from (1, 2) to (4, 7).

A:

Q: 1. Determine whether the lines L₁ given by z=t, y=1 with -∞ <t<∞o) and L₂ given by z=2+s, y = 3-2…

A: Introduction: If two lines are parallel then the ratio equality is true between them. And if two…

Q: Let l be the line (1, –1,1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l. %3D…

A: Given the line equation l is 1,-1,1+t0,2,1 and the point is Q=1,0,1. Find the distance from Q to l.

Q: The value of the line integral fydx + xydy over the straight-line path C from (0, 0) to (1, 2)…

A:

Q: Evaluate F- dr where F(, y, z) = (1.5yz cos(ryz), 1.5xzcos(ryz), 1.5xy cos(ryz)) and C (*) is the…

A: We need to evaluate the line integral between the two points.

Q: 2. Draw a line that is perpendicular to segment XY with point A, not on the segment A.

A: Solution

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

A:

Q: Compute f, f for f(z) = sin(5z) and path y that is the line segment from 3 – 6i to -6+ 6i.

A:

Q: 9. Find the point (x, y) on the line y = 2x + 3 such that the distance from (x, y) to (1, 1) is as…

A:

Q: Find equations for the lines tangent and normal to the cissoid of Diocles y (4 – x) = 9x° at (2,6).

A:

Q: Find the angle between the line given by ⟨x, y, z⟩ = ⟨2t, 3t, t⟩ and the y-axis exactly.

A:

Q: If C is the line segment which begins at (-2, 1) and ends at (2, 4), evaluate the line integral: et…

A:

Q: The value of the line integral I- [Adl where A-(2x+y)£+(y-x)ý along the parabola y=x^2 and form…

A: Evaluate: I=∫A.dl              ...(1)WhereA=2x+yx∧+y-xy∧

Q: Suppose L, is the line through the origin in the direction of u and L2 is the line through the point…

A: For first line L1, the line passes via origin, i.e., 000 and the line is parallel to u=110, so, the…

Q: Consider the points P(2, −1, 0), Q(5, 0, 0), and R(3, 1,√5). Find the coordinates of the point S on…

A:

Q: Evaluate the line integral 2ydx + 5xdy where C is the straight line path from (1, 2) to (6, 5). Г…

A:

Q: Compute x²z ds where Cis the line segment from (0,6,–1) to (4,1,5).

A:

Q: Find a parameterization, x = x(1), y = y(t), tE [0, 1], for the line segment from (2, -1) to (5, 5).

A:

Q: Find the shortest distance from the point (2,0, –3) to the plane x + y + z = 1.

A: This is a problem related to geometry part. Based on the concept of plane and point we will find the…

Q: Suppose that we start at the origin in the xy-plane and take n unit steps (i.e., each step is of…

A:

Q: Find the distance from the point (1,1,5) to the line X=1+t, Y=3-t, Z=2t. O (5)^0.5 O 7 O 2(3)^0.5 O…

A: Given: Equation of line is: X = 1+ t Y = 3 - t Z = 2t To find: distance from the point (1, 1, 5) to…

Q: Which of the following represents two lines that are coplanar and do not intersect?

A: We want to find the lines which are coplanar and don't intersect.

Q: Find the distance between the given skew lines: x = 4+9t, y = 5+ 3t, z = 7- 6t x= 8 – t, y = 9, z =…

A:

Q: et y = [ 2   3   -1] and u = [ 2   -6   -6] compute the distance d from y to the line through u and…

A: first we shall find equation of line then find distance from line of that point

Q: The distance between the two lines x = 1+ t,y = -2+ 3t, z = 4 – tand x = 2s, y = s, z = s is

A: Please see the explanation below

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: Let y = [3] and u = [2] to the line through u and the origin. Compute the distance from y

A:

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

A:

Q: 2- The distance d from the point R=(1,4,-3) to the line L: x=2+t,y%3-1-t Z- 3t is 4.43 False True

A:

Q: The equation of a line perpendicular to 4x+7y– 63 =0 is Oy- z 6 Oy--- I. Oy =z+

A: See the details solution in below

Q: 9. Reflect the point (3, 2) over the following axes or lines. Reflection Over New Coordinates x -…

A: Definition used -                    Reflection of a point over the x-axis -…

Q: Construct perpendicular lines from point P to line m. 1. VE

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: | 6. Let y = 3 and u = . Compute the distance from y to the line through u 1 2 and the origin.

A: Given: y=-231  and u=1-12 To compute: the distance from y to the line through u and the origin.…

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: Compute (x² + 2y + 3z +1) ds where Cis the line segment from (0, 2, 3) to (2, 5, 7).

A:

Q: Evaluate the line integral 3ydx + 6xdy where C is the straight line path from (1, 2) to (6, 5). Sc…

A:

Q: 7 ) Find the equation of line L through the point 5,,5 intersecting at right angle the 2 line M with…

A:

Q: ez ds where C is the line segment from (0, 6,-1) to (4, , 5). Compute

A:

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

A:

Q: Find the shortest distance from the point (1, 0, −9) to the plane x + 2y + z = 9.

A: Given plane isx + 2y + z = 9and point (1, 0, -9)We have to find shortest distance

Q: Let I be the line (1, -1, 1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l.

A: In a 3 dimensional space, a point and a line can be at infinite number of distance from each other,…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.