a) Prove that given lines are skew.  ?1: [x, y, z] = [1, 3, 7] + t[–1, 1, 2] ?2: [x, y, z] = [4, –2, 1] + s[3, 2, –5] b) Find the EXACT distance (do NOT round) between these two lines. please, step by step.

Q: Find the point R that breaks the directed segment Pe in a ratio of 1:3, given point P(-4,5) and…

A:

Q: In the figure at the right, WY bisects UV atY and UY bisects TW at X. For each situation, find the…

A: The figure is given as shown below: WY bisects UV at Y UY bisects TW at X We have to solve the…

Q: Find S. Re z?dz clockwise around the boundary of the square with vertices 0,j, 1 + j,1

A:

Q: Refer to the cube to indicate if the given lines are parallel, intersecting. neither. or S R T. 1.…

A: Given figure:-     To find:- Refer or neither. to the cube to indicate if the given lines are…

Q: Evaluate the line integral along the given path(s).

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

Q: 5.If A. B,and M are three collinear points,such that M clevides AB internally in the ratio 3:4 and a…

A: section formula for internal division  in vector form is OP→=nOP→+mOP→n+m According to the question,…

Q: 10. Find the coordinates of point P along the directed line segment AB. A(2, 0), B(12, -5) so that…

A: Here we have, point A(2,0) and point B(12,-5).AP:PB=3:2We have to find coordinate of point P.

Q: Which of the following is the distance from the point R= (1, 4, 1) to the line passing through the…

A: Option b is correct.

Q: Given the points M(-3,-4) and T(5,0), find the coordinates of the point Q on the directed line…

A: Q divides the line segment MT in the ratio of 1:3let the coordinates of the point Q be (x,y)

Q: Which of the following is NOT true about the following diagram? O Lines a and b appear to be…

A: Given figure :-

Q: Suppose P,Q,R,S are four collinear points such that: a. Q is between P and R. b. Ris between Q and…

A:

Q: Which of the following line segments is located in plane P? E B. CB BC OAE MacBook Air 000 000 DD 08…

A:

Q: .

A:

Q: 44. Use the cross product to find the area of the triangle with vertices P = (1, 1, 5), Q = (3, 4,…

A: If triangle T spanned by two non zero vectors u, v Then the area of the triangle is given by…

Q: Let points A; B , C , and D in R3 have respective coordinates (1, 2, 3), (−2, 3, 5), (0, 3, 6), and…

A: Given: A(1, 2, 3), B(−2, 3, 5), C(0, 3, 6), D(3, 2, 4)

Q: If V = Ai - j +sk and Vz= 41+2j +4k, Find Value of (A) so that the length of Projection of V ont Vz…

A: Use the formula for length of projection of a vector onto another vector

Q: 6. Use the Side-Splitter Theorem to find z given that NQ is parallel to OP. 2.5 5 M O 4 3

A: We have to find out

Q: Which of the followings are false? I. L, : x = 1 +t, y= -2+ 3t, z = 4 – t and L2 : x = 2s, y = 3+ 8,…

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Q: In AXYZ, m₂X = 27° and m2Y = 48°. Which gives the sides of the triangle in order from shortest to…

A: Given query is to find the side lengths order.

Q: Let AB be a segment and letr be its axis. Show that every point P on r is equidistant from A and B.

A: Consider a line segment AB and r be its axis. To show every point P on the axis r is equidistant…

Q: Let F = (z,2x, y) and C is the straight segment from (0,0,0, to (1,2,2). Then F• dř = %3D a) 7/2 b)…

A: Parametrize the line and then integration.

Q: Given the points A(-1, 2) and B(7, 14), find the coordinates of the point P on directed line segment…

A: Given: A(-1, 2) and B(7, 14) To find: The coordinates of the point P on the directed line segment…

Q: 1. Given that ZA, ZB, ZC, ZD e {angles} such that ZA and ZB are supplementary angles, ZC and ZD are…

A: It is given that ∠A and ∠B are supplementary angles, so we have: ∠A + ∠B =180o    ....   (1)   Also,…

Q: (c) Consider the parallelepiped with sides: u=(5,-2,1), v=(3, 2, 4), and w=(-6,1,1). V

A: Angle between two vector V and W found using cosine function

Q: 3) Consider the line L in R? spanned byp = (6). Let PL(u) be the orthogonal %3D projection of the u…

A: b = 4

Q: Let C be the line segment connecting 0 to ni. Then ſ. 1- e2zdz = %3D a. 0 b. -0.5 + ni C. πί d. None…

A:

Q: Evaluate 36e dz, where C'is the polygonal path Oto consisting of the line segments from z = 0to z =…

A: The given integral is                                       ∫C36ezdz,  where C is the polynomial…

Q: Let points A, B, C, and D in R3 have respective coordi- nates (1, 2, 3), (−2, 3, 5), (0, 3, 6), and…

A: A1, 2, 3, B-2, 3, 5, C0, 3, 6  &  D3, 2, 4. Now,…

Q: Given: line segment EF is parallel to line segment GH. Line segment AB parallel to line segment CD.…

A:

Q: Find the coordinates of point P along the directed line segment AB so that AP to PB is the given…

A: Given,          The coordinates of point P along the directed line segment AB so that AP to PB is…

Q: 1. On a coordinate plane, DEF has vertices D(1, 2), E(7, 2) and F(1, 9). What is the distance…

A: Since, distance bewteen two points is given by:-d=x2-x12+y2-y12

Q: In this exercise we find the area of a plane figure. Draw the parallelogram with vertices A(3, 5),…

A: Here we have to draw the parallelogram with vertex A(3,5), B(7,5), C(5,8), and D(9,8).  The graph of…

Q: Let P and Q be the points in R3, with respective coor- dinates (3, −1, 2) and (4, 2, −3). Find the…

A: P3, -1, 2  and  Q4, 2, -3.

Q: (c) Construct the locus lofpoints 3.5 cm from R and letl and PQ meet at l, andl (b) Construct a…

A: Here we will do given constructions,

Q: Find the coordinates of point P along the directed line segment AB so that the ratio of AP to PB is…

A:

Q: 7. Given the points A(-3, -4) and B(2, 0), find the coordinates of the point P on directed line…

A: Here given  endpoint of the line segment Ax1, y1=-3, -4Bx2, y2=2,0 A point P on directed line…

Q: Part (a) Evaluate 25e dz, where C'is the polygonal path consisting of the line segments from z = Oto…

A: Integration

Q: Find the coordinates of the point K that lies along the directed line segment from J(4,1) to L(8,11)…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Refer to the cube to indicate if the given lines are p parallel, intersecting. or neither. R U V T.…

A:

Q: The diagonals of rectangle QRST intersect at P. Given thạt m/PTS = 34° and QS = 10 , find MZSRT. 34°…

A: In triangle RST angle S + angle(srt) + angle  (rts) = 180 90 + angle (srt) +34= 180 Angle (srt) = 56

Q: Find the distances: a. Between 4 = (3+t,-2+ 3t,-t) and l2 = (1+ 2t, t,5+ 4t). %3D %3D b. Between the…

A: 3-d geometry is the concept that deals with 3 dimensional figures. In order to find distance between…

Q: In a plane, if line f is perpendicular to line m and then fln. mln f || n n || f m || n

A: In the question we have to choose correct option.

Q: Show that the two triangles are similar. S v and SVR Z V. so ASIVR ATRU ZVRS L

A: The figure given in the problem represents two triangles. From the figure, angle VRS and angle RUT…

Q: Let C be the line segment connecting 0 to ni. Then S, 1- e2 dz = а. О b. -0.5 + ni C. πί d. None of…

A: Let C be line segment connecting 0 to πi. Evaluate the integral ∫C1-e2z dz. Formula: Let γ be a path…

Q: Compute : fr (Re z – 3z) dz where r is a directed line segment from z = 0 to z = i .

A:

Q: 7) Given: Parallelogram ABCD with diagonals AC and BD intersecting at E. Prove: AADE ACBE B.

A: Solution: To Prove △ADE≅△CBE

Q: Find the point R that breaks the directed segment Pe in a ratio of 1:3, given point P(-4,5) and…

A: Here We will find the coordinate of the point R .

Q: Find the length of each segment. W X Y -5 5. WX 6. WY Wx= WY = MAXE 7. Points A, B, and C are…

A:

Q: Let C be the line segment connecting 0 to ni. Then S, 1- e22dz = а. 0 b. -0.5 + ni C. πί d. None of…

A: I have provided a solution in step2.

Q: If C is the line segment from (8, 4) to, (0, 0), find the value of the line integral: (6y? i + 5x})…

A: To solve the line integral from (8,4) to (0,0)

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.