Let a and m be real numbers, u = (1, a, 2, m, -3), and w = (2, а, 2, т, 3). Then the distance between u and w is:

Q: Prove that for any two points A and B, line segment AB = line segment BA

A: To prove that for any two points A and B, line segment AB = line segment BA.

Q: Let u = (2, 1, –1), v = (-4, 4a + B, 2), =(a,0, 3,8). %3| Find the values of a and 8 such that: u is…

A: Given: u=2,1,-1, v=-4,4α+β,2, w=α,0,3β; u∥v and v⊥w

Q: 16. Let y = and u = B Compute the distance from y to the line through u and the origin.

A:

Q: Write a two column proof to prove the following: If a transversal intersects two parallel lines,…

A: Given, Statement: If the transversal intersects two parallel lines then the bisectors of two…

Q: Which of the following would show that the diagonals of quadrilateral JKLM on the coordinate plane…

A: The given triangle JKLM is,

Q: Show that the points A(1, 1 + d), B(3, 3 + d), and C(6, 6 + d) are collinear (lie along a straight…

A:

Q: Let j = and i = Compute the distance from j to the line through u and the 9. origin.

A: Given that y→=-39 and u→=12. To find the distance from y→ to the line through u→ and the origin, we…

Q: 1 Let C = [c1, c2, c3] = -1 2 3 -1

A:

Q: ( , s) Let A = (-1,3) and B = (2, 4). Find the set of points C such that the area of triangle ABC is…

A:

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: Let y = and u = | Compute the distance from y to the line through u and the origin.

A: Compute the distance from y = [-3,9] to the line through u = (1,2) and the origin.

Q: The midpoint of AB is at (5, 0). If A = (4, 3), find B. B is:(

A: Consider the given information.

Q: A(-3, 2), В(5, — 4), С(7, 7)

A: Consider the given points,  Now, prove that C is on the perpendicular bisector of segment…

Q: Given: MT and HA intersect at B, MA  HT , and MT bisects HA. Prove: MA ≅ HT

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Q: Let u = (– 2, 4, 0) and v = (– 1,0, – 3). Find the angle 0 <0 < 180° (in degrees) between u and v.…

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Q: 8. Lines p and q are intersected by transversal t as shown. What value of x proves that linesp and q…

A: Follow the procedure given below.

Q: Show that the sum of the two perpendiculars drawn from any point in the base of an isosceles…

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Q: Suppose n is an integer and z-z =r is a contour traversed once in counter clockwise, then dz = 2 Ti…

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Q: Prove that C is on the perpendicular bisector of segment AB.

A: Solution:Given A(-4,-3), B(6,1) and C (5,-11)To Prove: C is perpendicular bisector of ABi.e., to…

Q: Find an eguaton for the set of all points (a sy, z) equiditant fom point (1,0,2) and

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Q: If (x, y) is any point on the unit circle, and t is the distance from (1, 0) to (x, y) along the…

A: x, y is any point on the unit circle and t is the distance from 1, 0 to x, y along the circumference…

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: (b) Let A(4,4, 7) and B(11,8, 11) be two points in 3D. Determine the coordinates of the point Q…

A: Introduction: When a vector is a non-zero scalar multiple of another vector, the two vectors are…

Q: If the point (p, q) , (m, n) and(p-m, q-n) are collinear show that pn = qm

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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  &amp;  D3, 2, 4. Now,…

Q: Let à = and b = . Find k so that a and b will be orthogonal (form a 90 degree angle) k-

A:

Q: Prove that all the points on a perpendicular bisector of a line segment AB are equidistant from the…

A: Statement:All the points on a perpendicular bisector of a line segment AB are equidistant from the…

Q: If P and Q are represented by the numbers z1 and z2 such that H- then the circumcentre of AOPQ,…

A: Given P an Q are represented by the numbers z1 and z2 such that |1z1+1z2|=|1z1-1z2| We need to find…

Q: Suppose n is an integer and z-z=r is a contour traversed once in counter clockwise , then P(z-z)" dz…

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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: Find the stundand matices * and a for ToT,OT and て:→ド,1)- (-3y, fn + 3) T:→ド, 1.(4)): (J,)

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Q: The midpoint of AB is at (2,5). If A=(7,0) find B

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Q: The three sides of a triangle are 5, x, and 8. Give all possible lengths x so that the triangle is…

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Q: If B, I, and T are distinct points of a line and point I is between point B and T, if BI = 5 mm and…

A: Given- If B, I, and T are distinct points of a line and point I is between point B and T, if BI = 5…

Q: Find the distance between u and v.

A: To find the distance between vectors u and v. We know that the distance between two vectors A=x1y1…

Q: If AB = –7i + 3j + 8k and A is the point (-2, –3, 6), find B.

A: To find the point B

Q: 2.) Example: Prove the Symmetric Property for the line segments. Given: PQ XY Prove: XY PQ P. Y Q

A: For the given line segments PQ≅XY

Q: If M is the midpoint of AB and AM = 12. then AB = _?_.

A: Given: M is the midpoint of AB.

Q: Let à = and b= . Find k so that a and b will be orthogonal (form a 90 degree angle). k=

A:

Q: show that if ||u||=||v||, and u and v are not parallel, then u+v and u-v are perpendicular.

A:

Q: The midpoint of AB = (1?), 1)

A: Find the midpoint of AB.

Q: Let ä = (4, 3) and b = (- 3, k). Find k so that ä and & will be orthogonal (form a 90 degree angle).

A: Given,            a→=&lt;4,3&gt;            b→=&lt;-3,k&gt;We know that,          For orthogonal,…

Q: Suppose n is an integer and z-z=r is a contour traversed once in counter clockwise, then dz 2 Ti if…

A: Since it is the standard result which is true for n=-1 which proof is given in next step.

Q: The midpoint of AB is at (−3,4). If A=(6,−3), find B.

A: The coordinates are ordered pairs with the x value listed first.The change in the x position is…

Q: Consider the points P(1,2,2), Q(−1,3,1),R(1,2,−3) and let A be the area of triangle PQR. what is…

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Q: (a) is the pazint (2,-2, 1s The point (2, I, 5) on the ime? explain ) fiad he paint where the line…

A: This is a problem of 3D geometry and parametric forms of straight lines in 3D.

Q: Let ä = (– 3, – 2) and 5 = (1, k). Find k so that ä and b will be orthogonal (form a 90 degree…

A: Two vectors a→ and b→ are orthogonal if their dot product is zero, because both the vectors are…

Q: Suppose you are given a line l and a triangle AABC such that A, B, and C do not lie on l. Prove that…

A: