d) Find the norm of v. i) v =< -1,2,4 > ii) v = -i + 7j

Q: For any geometric vectors u and v, prove the following using triangle inequality. (a) ||u – v|| <…

A: a) llu-vll ≤ llull +llvll b) llull - llvll ≤ llu-vll

Q: 3) Write a two column proof. Given: ABCD is a parallelogram AABD = ACDB Prove:

A: We can prove the same as below.

Q: Find the value of k such that vectors x

A:

Q: Let a = ci + j and b = 9i + 63j. Find c so that a and b are orthogonal. C = i

A: Let's find.

Q: Among all unit vectors u = in R°, find the one for which the sum x + 3y + 8z is minimal.

A:

Q: ) Given : Quad rilateral RSTV with diagonals RT and su intersecting at w Prove : mLT+mLa= m23 tm<4

A: In the quadrilateral,                  ∠VWR=∠TWS.

Q: Write a two-column proof to show that if two consecutive sides of a parallelogram are congruent,…

A: Given:ER ≅ AV∠REA ≅ ∠VAE∠REO is a right angle triangleProve:RAVE is a rhombus

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 statement is true? O All squares are parallelograms. All rectangles are squares. O All…

A:

Q: Use the Trapezoidal Rule to estimate the number of square meters of land in a lot, where x and y are…

A:

Q: 9) Write a two column proof. Given: ABCD is a rhombus.

A:

Q: 14. Write a two-column proof. Given: PSTV is a parallelogram. PQ = RQ Prove: ZSTV= ZR P R.

A:

Q: Find the Euclidean norm of the given vector. 10 v = 24 Hint: 102 = 100, 242 = 576 ||v|| = Ex: 1

A: Given vector is: v=1024

Q: Find the length and direction (when defined) of u xv and v×u. u= - 8i – 4j – 3k, v = 3i + 3j + 4k

A:

Q: Calculate the area of the triangle defined by u = (1, 6, 2), v = (3, 0, 5). [A3]

A: Here we have to calculate the area of the triangle having vectors,  u→=(1,6,2) and v→=(3,0,5)

Q: II. Use coordinate geometry to prove that the diagonals of a rectangle. congruent. are

A:

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: 26. Write a two-column proof. Given: ABCD and AFGH are parallelograms. Prove: ZC = ZG A'

A: if two lines are parallel then crossponding angles  are equal

Q: Let a = ci + jand b = 7i + 49j. Find c so that a and b are orthogonal. C = i

A:

Q: 2. Let ū= , i = . Fine a. u.v proj. c. Angle between u and v d. Cross product uxv e. Verify that uxv…

A:

Q: Create a two-column proof. B A D Given: Rhombus ABCD with diagonals AC and BD intersecting at point…

A: Properties of the Rhombus -  Rhombus has four equal sides and opposite sides are parallel.…

Q: 19.Write a two column proof. Given: ABCD is a rhombus. Prove: AADCE ABCA C

A: We have to find out

Q: Let a = ci + jand b = 7i + 35j. Find c so that a and b are orthogonal. C = i

A: Dot product of two vectors

Q: 4. Prove the following. Given: Parallelogram ABCD; Z BAD = L CBD Prove: AABD is isosceles A…

A: Given □ABCD is parallelogram,Given ∠BAD=∠CBD                            (1)Aim : △ABD is isosceles…

Q: Write a two-column proof to demonstrate that the diagonals of the trapezoid below are congruent.…

A: Given :VW¯≅YX¯∠WVY=∠XYV To prove:VX¯=YW¯

Q: d) Prove that ||vxw||²+|v-w[? = ||v||²|w||² for all vectors v, w in R3

A: Prove the following

Q: Show that quadrilateral ABCD is a parallelogram by verifying the given criteria. B. C A 8. Verify…

A: We have to show ABCD is a parallelogram

Q: Write a two Column proof. Given: Parallelogram JKLM Prove: AJKM ALMK 21. K

A:

Q: a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal, (b) Draw a diagram…

A: a) Suppose u,v are orthogonal. Now…

Q: The norm of the set {cosh(i nn x},n E N, –-2<x<2 in the Hermitian sense is:

A: Given,                  cosi nπx, n∈ ℕ, -2≤x≤2

Q: Find the norm of vector v3(3,0,1,4) in R a. 10 b. 15 C. 20 d. 26 OOO0

A: The given problem is to find the norm of the given vector in R4. Given vector v=(3,0,1,4).

Q: Every trapezoid has two parallel bases. O True False

A:

Q: 6. Let AABC be a triangle and let D, E, and F be the midpoints of the sides BC, AC, and AB,…

A:

Q: Let a ci + j and b 2i + 6j. Find c so that a and b are orthogonal. C =

A:

Q: In quadrilateral ABCD,∠1=∠2 and ∠B=∠D.  Prove that ABCD is a parallelogram. Use two-column proof

A: In this question we have to proof that given quadrilateral is parallelogram.

Q: Make a two column proof of the following R Given: TP is a diagonal of the parallelogram TSPR Prove:…

A:

Q: Find the Euclidean norm of the given vector. Hint: 7 = 49, 24? = 576 V = 24 ||v|| = Ex: 1

A:

Q: Write a two column proof. Given: Parallelogram JKLM Prove: AJKM= ALMK 21. K

A: We can prove the question as below.

Q: Given: B and D are midpoints of the sides AC and CF, BD = DE Prove: BD || AF. (Use two-column…

A:

Q: Find the norm of U = V + 3W V(9 , 10 , 1) and W(8, -4,-9)

A: The given two vectors are V=(9, 10, 1) and W=(8, -4, -9). Evaluate U as follows. U=V+3W=9, 10, 1+38,…

Q: Find the norm of v, and a unit vector that is oppositely directed to v. (a) v = (3, 3)

A: The given vector is v = 3, 3

Q: 7. Prove that R² is Hausdorff. Is R?T3? Is R?T4?

A:

Q: Draw a diagram showing u, v, u + v, and u - v in R2 and use (a) to deduce a result about…

A:

Q: let A= and Describe the sed of all vectors b for which the equatiön AX=b is Consitent.

A:

Q: 24. Determine m24 in the rhombus below. F 1 65°) 4 2, H. E m24 = 65° m/4 = 32.5° O m24 = 90° O m24 =…

A:

Q: Find the Euclidean norm of the given vector. v = Hint: 3? = 9, 4? = 16 ||v|| = Ex: 1

A: Given vector

Q: е. ZBCA and ZACD are a linear pair. f. AF and BD are perpendicular.

A:

Q: 7. What additional piece is needed to prove JMLK is a rhombus ?

A:

Q: For what values of aare u and v orthogonal?

A: Consider the given vectors  u=11-2  and  v=a-12 Write the vectors in row form u=1,1,-2  and…

Q: Use the Trapezoidal Rule to estimate the number of square meters of land in a lot, where x and y are…

A: