the tip being the point (3, 0, -5) E R' is awayfrom the line spannedby w= -2 3.2 1.2 as in this diagram -0.8 -2.8 -4.8 -6

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

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Q: Find the length of the curve over the given interval. r = 8, [0, π/6]

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Q: C is the line segment from (4, 2) to (0, 0) followed by the line segment from (0, 0) to (-4, 2).…

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Q: Find the coordinates of the intersection points A and B, between the closed curve (x + 1)² + 4(y-1)²…

A: In this question, we can find the intersection points of the given curve. Using the equation of…

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: are two points find d.c's of OP, QO and PQ where O If p(2, 3, 6), Q(3,4, 5) is the origin.

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Q: The equation of the tangent line to the curke x? + y = 36, at (6,-16) is %3D y = (x+6) + 16 16 16 16…

A: we have to find the equation of the tangent line to the given curve at (6, -16)

Q: Evaluate [(-x+y + 2)dx + (x+y-2)dy + (x-y+z) dz where C is the line segment from (-1, 2, 3) to…

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Q: The line that passes through the points (2,0), (0,1) is x+2y = c, where c = 1. O True False

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Q: Now compute [(x − 3y² + 2) ds where C' is the union of the curves C1 and C2. C1 is the line segment…

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Q: Evaluate S.(x – 3y² + z) ds for each of the following curves.

A: To find the line integral for given curve C, first we parametrize the the curve in term of t which…

Q: Find the point(s) on x = 3 - y that are closest to point A = (1,0).

A: Given: Curve x=3-y2 and a point A(1,0).

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

A: The given point S(0, 0, 0) The given line passes (-1, - 1, 2) parallel to v = 3i + k

Q: Find the distance from the point S(0,0,12) to the line L: x = 4t , y = -2t z = 2t 3

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Q: Find the distance between the point (−3, 5, 1) and the line given by x = 1 + t, y = 5 − 2t, and z =…

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Q: Suppose that P is twice as far from (0, 0) as P is from (6, 0 Find such a point on the x-axis.

A: Let A0,0 and B6,0. It is given that P is twice as far from A0,0 as from B6,0. We know that if point…

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: Find the point on the line y = 3x + 5 that is closest to the origim %3D (x, y) = %3D

A: We have to solve

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 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: C is the line segment from (4, 2) to (0, 0) followed by the line segment from (0, 0) to (-4, 2).…

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Q: Find the points on the graph of circle defined as (x – 1)2 + (y + 3)2 = 16 where the normal line is…

A:

Q: The equation of the line segment from A(3, – 4,4) to B(5,2,5), 0<t<1 is a. r= (3+ 2t)i +(- 4+6t)j+(4…

A: Topic = vector  correct option 'a'

Q: 2. Approximate f,(3,5) using the contour diagram of S(x, y) in Figure 14.9.

A: Given query is to find the value of fx(3,5).

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: The line that is normal to the curve x2 + xy - 2y? = 0 at (3,3) intersects the curve at what other…

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Q: What is the equation of the circle concentric with circle(x-2)2 + (y+1)2 = 5 that is tangent to the…

A: Explanation of the answer is as follows

Q: Evaluate.(2y dx + 4zdy + 3x dz)where C consists of the line segment C, from (1, 0, 0) to (4, 5, 6),…

A:

Q: Find the point(s) of intersection of the curves r = 10 and r = 20 cos e. O A. (10,5) 3 OB.…

A: Given: r = 4  r = 20 cos θ

Q: The area bounded by the curve y= 4x and the lines r = 7,1 = 10 and x - aris is O 4900 square units O…

A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

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

A: We are given two lines L1 and L2 in 3d, and we have to find the closest points x1 , x2 such that the…

Q: The line that is normal to the curve x + 2xy - 3y = 0 at (4,4) intersects the curve at what other…

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Q: 2 Show that the line y = x +3x+m for all values of m. y= mx+4 will touch or intersect the curve

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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: 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: 10. In the standard (x, y) coordinate plane, line r contains the points (6, 5) and (b,-5), and line…

A: Given problem is :

Q: 5. Find the point of intersection of the following lines x = 4t +2, y = 3, z = -t +2 b. x = 2s +6, y…

A: Given query is to find the point of intersection of line a and line b.

Q: Find the line through (1,-1,1)and normal to the line  3x=2y=z , and parallel to the plance  x+y-z=0…

A: Equation of the line: The equation of a line passing through the point (x0, y0, z0) is given by (x,…

Q: What is the sum of the abscissas of the points where the tangents of the y=(1/3) x^3-(3/2) x^2 – 2x…

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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: 3. The equation showing a family of lines passing through the point (1, -1) is given by * у%3D тх —…

A: Given a point(1,-1). We need to find the equation of  a line passing through the given point.

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

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Q: Suppose that dy xy + x d.x and that the point (5,0) lies on the graph of (x, y). What is the value…

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Q: Find the length of the curve ƒ1x2= x3&gt;2 between x = 0 and x = 4 (as shown).

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Q: The area bounded by the curve y = 10z and the lines z = 9,7 = 11 and a – azis is O 1010 square units…

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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: 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,…