21-24 - Area of a Parallelogram Find the area of the parallelo- gram determined by the given vectors. 21. u = (3, 2, 1), v = (1,2, 3) 22. u = (0, –3, 2). v = (5, -6, 0) 23. u = 21 - j+ 4k, v = ļi + 2j – k 24. u = i - j+ k, v = i+j-k

Q: *₁ = (1, 2, 3), 2 3. Find the angle between the two planes 3x + y + z = 4 and 2x + 3y + 2z = 3 using…

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Q: 4. Three collinear vectors, a, b, and c, are such that à = 2²/b b and à = 1/2c. (a) Determine…

A: The objective of the question is determine the knowns.

Q: Find a nonzero vector u with initial point P(2,-3,6) such that (a) u has the same direction as v =…

A: Given: A non zero vector u with initial point P(2,-3,6) To find:  (a) u has the same direction as v…

Q: 4. Prove that the vectors a= (1,1,1); b-(1,-1,0) and e-(-1,-1.2) are orthogonal to each other! 5.…

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Q: The plane that contains the points (-2, 1, 0), (1,0, – 1) and (0, –1, 1) is orthogonal to which…

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Q: 1 %Define the three vectors u=[1, 0, -4], v=[3, -3, 1], and w=[0, 2, 1]. u=[1 0 -4] v=[3 -3 1] w= [0…

A: ##Importing the library of numpy and then Defining the 3 vectors : import numpy as np…

Q: 10. Find two unit vectors orthogonal to both v = (3, 1, 1) and w = (-1,2, 1). 11. Find the area of…

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Q: Find two non parallel and two parallel vectors both orthogonal to (1, 2, 3)

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Q: = 2. Are the vectors V = (2, — 4, 1) and w Show work and briefly explain. (3, 2, 2) orthogonal? 3.…

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Q: 3–8 - Cross Products For the given vectors u and v, find the cross product uX v. .3. и %3D (1,0,…

A: 3).  Given u=1,0,-3, v=2,3,0. To find the cross products. Solution: Finding cross products of given…

Q: 18!- Use the vectors to find the area of the triangle with vertex A(1,0,1), B(0,2,3) and C(2,1,0).

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

Q: 9. Consider the column vectors u and v in R" cos(0) cos(20) sin(0) sin(20) u = v = cos(n®). sin(nº).…

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Q: how can one show that three vectors span R^3?

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Q: 1- Find the distance d between the points (4 ,6, – 1) and (8 , -2,6) 2- if v =(-4 ,0,2) and w = (6,…

A: We have given vectors, we have to find  1. Distance between points.  2. 2w-4v 3. P2 P1 4. Unit…

Q: 5. If we have two vectors (V₁ and V₂), V₁ is a vector perpendic through the points A(1, 2, 5),…

A: Introduction: When a vector is along the direction in another vector, the two vectors are parallel…

Q: 7) Find a vector that is orthogonal to the plane that contains the points P(1,–2,4), Q(-2,3,2), and…

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Q: (2,1, –4,0), v = (-1,-1,2,2), and 19. Find two vectors of norm 1 that are orthogonal to the vectors…

A: We have to find the basis of these vectors, which are independent. A=2-131-12-425024~I4 and they all…

Q: What is the volume of the parallelepiped with sides 6i + 9j + 5k, 2j + 5k, and 10k? volume = Find a…

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Q: (1) Choose two vectors v1, v2 in R 2 and another vector b also in R 2 . Find scalars x, y in R such…

A: (1) To choose two vectors v1, v2 in R2  and anther vector b also in R2 such that xv1+xv2=b, x& y…

Q: 11. Given đ = (2, x, –3) and b = (5,–10,y), for what values of x and y are the vectors collinear?

A: We have to find the values of x and y for which bothe the vectors are colinear

Q: 6. We have two vectors: a =) and b= 8 What is the resultant of -a plus b? (

A: Given:     To find: -a + b

Q: 5. Choose ONE strategy shown in class to verify that the vectors: = (1.3, -1).5, = (2.1,1)and i, =…

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Q: 9. A rectangle is formed in R² by the vectors OA = (1, 3) and OB = (6, –1). a) Calculate the…

A: a)Given OA=i+3jOB=6i-jSince OC is diagonal of parallelgram ABCDOC=OA+OBOC=i+3j+6i-jOC=7i+2j

Q: 9. Let ū = (4, -6), T = (-2,4), and = (6,4). (a) Are ī and ū orthogonal vectors? How about ĩ and w?…

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Q: Choose two vectors v1, v2 in R^2 and another vector b also in R 2 . Find scalars x, y in R such that…

A: As per our guidelines, since you have asked multiple questions, we will solve the first question for…

Q: 6. Find the angel between two vectors ī= (-1, –1,2) and w= (2,3, –2). %3D

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Q: Show that u1 =(1, 0, 0, 1), u2= (−1, 0, 2, 1), u3= (2, 3, 2, −2) and u4 = (−1, 2, −1 , 1) is an…

A: The given set of vectors are: u1=(1, 0, 0, 1)u2=(-1, 0, 2, 1)u3=(2, 3, 2, -2)u4=(-1, 2, -1, 1)

Q: Find two different combinations of the three vectors u = (1, 3) and v = (2, 7) and w = (1, 5) that…

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Q: 4. 5. Find the dot product of u =(5,10) and v= (19,-9) Are the vectors u = (12,-3) and…

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Q: 1. Find the unique unit vector ī = (v1, v2, v3) that is orthogonal to (1, 1, –2), forms an angle of…

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Q: 5. (a) Are the vectors (1,3, 2), (2, 1,3) and (3, 2, 1) linearly independent? (b) Are the vectors…

A: Explained below

Q: 2. If ā = 3i - 27 + ok and b =(4,-1,-6) compute ā xb. 3. Find a vector that is orthogonal to the…

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Q: Find the equation for the plane through the point Po= (9,2.5) and normal to the vector n= 31 + 10j +…

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Q: Find the area of the parallelogram with vertices K(1,2,3),L(1,3,6),M(3,8,6), and N(3,7,3)

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Q: 1. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors (2,…

A: We need to find r.

Q: -2 - [109]. V. 6 Let V1 dependent. Upload Choose a File -3 V2 = 20 k Find the values of k for which…

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Q: 7 For what value of k are the vectors u Select one alternative: Ok=-1 Ok=-2 Ok=1 Ok=2 (1,-1,-1) and…

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Q: If vectors u =(3, 3), v=( 13. -7), and 2w +3u-v=(4,-4) what is the coordinate of vector w?

A: The given vectors are: And, Let the coordinates of vector w be, Substitute the coordinates in…

Q: A sum of scalar multiples of two or more vectors (such as c,u + c,v + c,w, where c, are scalars) is…

A: Given i=1,0 and j=0,1

Q: Find the angle between the vectors (approximate to the nearest degree): u = [0, 1, 1] and v = [1, 2,…

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Q: Let R, have the Eucidean inner product. Find two unit vectors that are orthogonai to all three…

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Q: 4. Find a vector that points in the opposite direction as ā = (-3,–14,2) with a magnitude of 32. 5.…

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Q: Find two unit vectors orthogonal to both (2, 3, 1) and (-1, 1, 0). LO î + 27 (F (smaller i-value) î…

A: Use the given information.

Q: a linear combination of the vectors Can we express the vector a = (2, – 5, 3) as e = (1, 1, 1), ez =…

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Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: as per the rule we are authorized to provide the answer for only one question so please provide…

Q: 8. a. Using the vectors = (3, 3, 1) and ỷ = (-1, 2, –3), verify that the following formula is true:…

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Q: 2/3 The vectors U. (c", b,3), V = (vE ;2,!) are parallel. %3D Find the norm of vector ū

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

Q: 1. The cross product of the vectors u = (a,, az, az) and v (bı, b, b;) is the vector ij k| u X v =…

A: given,         u=a1,a2,a3 and v=b1,b2,b3   and u=1,0,1 and v=2,3,0