Diagonals of parallelograms Two sides of a parallelogram are formed by the vectors u and v. Prove that the diagonals of the parallelogram are u + v and u - v.

Q: If a statement is true for all nonzero three-dimensional vectors a, b, and c, write "TRUE" on the…

A: TRUE statement is    The cross product is anti-commutative        TRUE statement is

Q: 43. Explain the differences between vectors and scalars. Provide an example of each. 44. Copy the…

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Q: Specify the unit vectors a = 2i + 3j-k and b = 3i + 4j.

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Q: angle betw 2. Determine whether the vectors a and b are parallel, orthogonal or neither for the…

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Q: Find the area of the triangle with vertices (1, 7, -9), (-2,-2,-9), and (-3, 1, -8). Then find both…

A: The Given vertices are:-   A1,7,-9, B-2,-2,-9, C-3,1,-8   AB→=-2-2i⏞+-2-7j⏞+-9+9k⏞ AB→=-4i⏞+-9j⏞+0k⏞…

Q: linear algebra  Write the vector 2i −j + 3k as a linear combination of the vectors i + 2j ,  2i - k…

A: We use the definition of linear combination of vectors to answer the given question.

Q: . Refer to vectors v and w in the figure.  a. Sketch v - w by placing the initial point of - w at…

A: 1.

Q: Given a = [1,3,-2] and b = [-2, 5, 1]. %3D Determine: a)The magnitude of the sum of the given…

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Q: 3. (a) Explain why there is no vector i such that (3, –1, 4) × J = (-5,1, –4). (b) Explain why there…

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Q: olve the vector product and scalar product of two vectors a = (1, 2, 3,) and b = (3, -2, 1)

A: Given a=i+2j+3k b=3i-2j+k

Q: A parallelogram is formed by the vectors [1, 2] and [3, -4]. Find the area of the parallelogram. O…

A: Given query is to find the area of parallelogram.

Q: Vectors F, 5, E, and u are shown on the coordinate plane below. y 6- -6 Select the correct column…

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Q: Find a so that the vectors v=i-aj and w = - 10i+ 7j are orthogonal. a = (Type an integer or a…

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Q: Vectors. 3U-4v U=6,7 and v=6,-7

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Q: Find the area of the parallelogram that had the given vectors as adjacent sides. Use a computer…

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Q: 21-24 - Area of a Parallelogram Find the area of the parallelo- gram determined by the given…

A: (21) Given vectors are u=3,2,1 and v=1,2,3 Area of the parallelogram =u×v…

Q: A parallelogram has diagonals determined by the vectors. Show that the parallelogram is a rhombus…

A: Given: A parallelogram has diagonals determined by the vectors d1=220 and d2=  1-1  3

Q: Area of a Parallelogram Find the area of the parallelogram determined by the vectors u = (4, 1, 1)…

A: Given vectors are u=4,1,1 and -1,2,2. Area of parallelogram=u×v…

Q: Compute the dot product of the vectors u and v, and find the angle between the vectors. u= (-14,0,6)…

A: we have given two vectors  u=-14,0,6=-14i+6kv=1,2,3=i+2j+3k

Q: 10. Given vectors ū =[-3,2,–6]and v = [5,0,8], find a) a vector on the x-z plane, and perpendicular…

A: As per our guidelines I solved first three subparts so kindly request you to repost the remaining…

Q: Perpendicular vectors Show that two nonzero vectors u = (u, uz) and v = (Vị, v2) are perpendicular…

A: we have to show that two non zero vectors u=u1,u2 and v=v1,v2 are perpendicular to each other if…

Q: a,b,c are all vectors. For the vectors:  a = 3i+4k ; b = 2i-j ; c =i+j-5k calculate: 1) vector c •…

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Q: 24. Diagonal of parallelogram Show that the indicated diagonal of the parallelogram determined by…

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Q: Linear Algebra  find a representative of x (vector)

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Q: Use vectors u= (-4,1) , v= (5,-2), and w= (0,6) to perform the indicated operation. Then determine…

A: The given vectors are: u=-4, 1v=5, -2w=0, 6

Q: 4 2- 5 -4 -3 -2 -! -2- -3 -4 Find the components of the addition of the two vectors u and v shown.…

A: To find the addition of two vectors u and v

Q: True or false?(a) The vectors v and −2v are parallel.(b) The vectors v and −2v point in the same…

A: The vectors v and −2v are parallel. Since the corresponding components of the vectors v and −2v are…

Q: vectors u = -2i+4j-√√5k and v= 2i-4j+√5k, find: 1. the vector proj,u 2. the scalar component of u in…

A: Here we will solve both the sub-parts step by step,

Q: : (2,1,2). 1- Find the unit vectors u1 and u2 in the directions of v = (1,3) and w = Find unit…

A: If we have a vector u=a,b,c, then the unit vector that is in the direction of vector u is the vector…

Q: Consider vectors v, w, and w: u = , v = , w =   Find the triple scalar product u · (v ⨯ w)

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Q: 2) Let ā = (),: = ), c = (_ be 3 vectors. a) Write 2b – č as a column vector. b) Saif says that the…

A: we have given three vectors . We have to write the following

Q: 4- Parallel and perpendicular vectors Let u = 5i -j+ k, v = j - 5k, w = -15i + 3j - 3k. Which…

A: We will find which vectors are perpendicular and which are parallel as following.

Q: Two vectorsu and v are given. Find their dot product u · v. u = (-2, 0, 2), v = (2, 3, ) %3D

A: Given that u=-2, 0, 2v=2, 3, 12To determine u.v

Q: Determine the scalars K and S that make the vector u a linear combination of the vectors v and w.…

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Q: a State the condition(s) that a, b, c, and d must satisfy for the vector b to be 1 1 -1 and spanned…

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Q: Scalar triple product Another operation with vectors is the scalar triple product, defined to be u ⋅…

A: Vectors u, v and w are coplanar if they lie on the same plane.  First, suppose that u, v and w are…

Q: = (3,2,1), b = (-1,2,2), and c = (-2,4,1): Given vectors a = a) What is ä – 4b + 3č? b) What is the…

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Q: compute the dot product of the vectors u and v, and find the angle between the vectors. u= (-…

A: Given :  u = ( - 14 , 0 , 6 )  and  v = ( 1 , 3 , 5 )   Find : dot product of two vectors and angle…

Q: a) Find the area of the triangle with vertices A(-2,5,1), B(3,-5,-2) and C(3,2,-4) using vector…

A: see below the answer and calculation

Q: Find the vector w of length 4 in the direction of v = 7i + 4j. (Give your answer using component…

A: NOTE: Refresh your page if you can't see any equations. . find the norm of the vector

Q: Find a unit vector orthogonal to the vectors 5i + 8j + 3k and 4i + 8j + 8k with non-negative first…

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Q: 7-8. Vectors in the same direction are always parallel.

A: 7-8     two vectors U , V are parallel if there cross product is zero.        now U*V = |U| |V|…

Q: 42. Area of a Parallelogram Find the area of the parallelogram determined by the vectors u = (4, 1,…

A: Area of parallelogram = u X  v

Q: A taxi has 2 passengers when it starts at A. It must drop off one person at B and the third at C.…

A: A taxi route is from A to B to C.  In the below figure: All square blocks are of same edge length.…

Q: 7. and V -8 are orthogonal. 15 The vectors u = %3D L-7 True

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Q: Find the area of the triangle with vertices (-3, –7, –1), (–10, –8, –1), and (-7,–1,–6). Then find…

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Q: Suppose we have three points in 3D space: P = (1,0, 1), Q = (2, 1, –1), and R= (0, –1,3) (a) Find…

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: Quéstion 4 The Vectors u= (2,5, 3) and v= (2, 1,–3) are orthogonal to each other. True False

A: Using property of orthogonality,

Q: Find the dot product and cross product of the given 2 vectors. Sketch the 2 vectors in x, y, z…

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