lem 17. What multiple of a = (1,1,1) is closest to the point b= (2,4,4)? Find also the poin st to a on the line through b.

Q: 2. The midpoint of the line segment between Pi (x, y) and point P2 (-2, 4) is Pm (2, -1). Find the…

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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: O Find the shortest distance from (1, 2, 3) to the line x = 3+t, y = 1 – t, z = 6 - 2t.

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

Q: 4. Find the distance between the two points S(-5,-2) and T(-3,4).

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Q: 4. In ARST, RU US and RV VT, If UV, the midsegment, is equal to 2x- 2 and ST = 8x - 28, find the…

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Q: Suppose I tell you that the line ax + 4y = 12 is parallel to the line 9x + ay = 17. Find all…

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

A: Given : Point A ( -3,1,5) x = 5+t  y=1-2t  z=3-t

Q: For what value of k will the line kx + 5y = 2k be perpendicular to the line 2x - 3y = 1?

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Q: Find the point (xo, yo) on the line 4x + 9y = 12 that is closest to theong1n.

A: Given: 4x+9y=12 Let the distance between the point (x0, y0) and origin be D As it is given that the…

Q: 10. Determine the point on the line x + 2y = 2 that is closest to (0, 0). Draw a sketch.

A: point which is closest to origin

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: 4- Find the line that passes through the point l2) the Point of intersection of the lines x+2y=3 and…

A: 4.  The equation of the line passing through a point x1,y1=1,2 and the point of intersection of the…

Q: Suppose point T is between points R and V on a line. If RT = 6.3 units and RV = 13.1 units, then…

A: Solve for TV

Q: 2. Find the angle between the lines 3x – 5y = 11 and 6y – 10x = 3.

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Q: Find the distance from the point S(1, 1, 5) to the line L: x = 1 + t, y = 3 – t, z = 2t.

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Q: 3. The line L is parallel to the line x t, y 2t, z =3 and passing through the origin.

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Q: What is the value of a if the point (a, – 1) is on the line 3x – 2y = 8? a =

A: We have to find the value of a.

Q: For what values of a  and b  is the line 2x  + y = b tangent to the parabola y = ax 2   when x = 2

A: Given line is 2x+y=b Given line can be written as y=-2x+b On comparing with equation of line y=mx+c,…

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: The line y 을 16 has x-intercept 3. -8)-and is perpendieular to Ahe line Passes through (4,pand…

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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: 2. the live in IR and haring Passing through He oryin as it's divechor vecter intersects the line…

A: The line in IR3 passing through the origin and having 1u3 as it's direction vector intersects the…

Q: 1. Find the point on the line y = x nearest to the point (4, 1).

A: Since, we have been asked to solve part(i) which aims to findthe point on the line y=x nearest to…

Q: If C is the line segment connecting the point (x1, Yı) to the point (x2, Y2), find the following. x…

A: “Since you have asked multiple questions, we will solve the first question for you i.e. (a). If you…

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: 4. The tangent of the acute angle between the lines y= 4x- 3 and y=x-5 is А. 5 В. C. 3 D. 5

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Q: Find the the point on the line l: +t 0 | closest to the point P(3, 2, –2). ||

A: The given line is                             l: xyz=101+t00-1 and a point         P(3,2,-2)

Q: Find the length of the curve given by r(t) = for -5 <t<5. O 5/19 O 10/10 O 10/19 O 5/10 O 10

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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

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Q: 4 - Which of the following is the shortest distance from the point (5, 0) to the curve y = V2x ? 7…

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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: FT [f'lt) = jwF(W) F(w) = jw f(w) => JA -T T tax + √(-_^) -jut e (-A) ²-just, AT Sim ² (WI) WT T A […

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Q: Given the point S(2, 2, –5) and the line x = 2+ 3t ; y= 3 + t; z=1– 2t Find the distance from the…

A: Given that the point S(2,2,-5) and the line x=2+3t; y=3+t; z=1-2t . Here we have to find the…

Q: 2. Find the distance between the parallel lines: L: 2x- 5 y + 3 = 0 ; (Hint: It suffices to compute…

A: Consider the given equations of the lines, L1: 2x-5y+3=0 and L2: 2x-5y+7=0 The formula of the…

Q: 2. Find for x? +x+ y? +2 3xy the lines that are tangent and normal to the curve at point (3,2).

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Q: on the line ye -2x +8 that 1-) Find the point IS Close't to the onigin.

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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: Which of the following points does NOT lie on the line x + 3y = 10? %3D O (-4, 14/3) O (-2, 4) O (2,…

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Q: Which of the following lines is perpendicular to the equa y=-2x + 8 Ox+2y = 8 O x- 2y = 6 O 2x-y = 1…

A: Perpendicular line

Q: B is the midpoint of line segment AC. Find x C 5X-6 3X +4 Ox = -5 O x 2 Ox = 5 Ox = 10

A: A line segment is a finite section of a straight line. A mid-point of a line segment is a point…

Q: 2 14 - For what value of K is the line 2x+ky = 3 Perpen odicular to the line 4x+y=12 For what the…

A: We will find to the value of k when  the line ,2x+ky = 3 perpendicular to the line 4x+y=1 . And olso…

Q: Question 15 Find the distance from S= (1,1,5) to the line L: x=1-1, y=2-t, z=31.

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Q: Find he value of ds/du at u = 2 if s t2 + 5t and t = (u? + 2u)

A: ds/du=9/2

Q: Find Sc((x² + 3y)i + 3y³j) · dr' where C consists of the three line segments from (2, 0, 0) to (2,…

A: Given ∫x2+3yi→+3y3j→.dr→ where C consists of the three segments from (2,0,0) to (2,2,0) to (0,2,0)…

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).

A: Given curve is fx=x32. To find the length of curve between x=0 and x=4. Solution: We know that…

Q: 16. If the lines y = 3x + 1 and 2y = x + 3 are equally inclined to the line y = mx + 4. Find the…

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