Is the following statement correct? If A, B, C, and D are distinct nonzero vectors represented by arrows from the origin to the points A, B, C and D respectively, and if B - A = C - D, then ABCD is a parallelogram. Draw a diagram to show if true or false.

Q: Given the points A: (2,4,-3) and B: (2,-3,5), find the vector ā AB

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Q: .If the position vectors of the points A, B, C, D are a = i+j+k, b 2i + 3j, c= 3i+ 5j - 2k, d k-j.…

A: Given:  a=i+j+k, b=2i+3j, c=3i+5j-2k, d=k-j We know that if A=x1i+x2j+x3k, B=y1i+y2j+y3k then…

Q: Compute the indicated vectors and also show how the results can be obtained geometrically. b-c

A: Given: b=23, c=-23

Q: For what values of b are the given vectors o , (smallest value)

A: Let m→=-12, b,3 and n→=b, b2,b  If m→ and n→ are orthogonal.

Q: It is known that the area of the parallelogram P formed by the vectors u and V is 14 square units…

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Q: In triangle ABC a line is drawn from A to the midpoint of BC, labelled D. Prove that vectors…

A: The solution is given by using triangle law of vectors as follows

Q: If vectors have the same magnitude and direction, then they are_____.

A: We have to fill in the blanks: If vectors have the same magnitude and direction, then they are…

Q: If two vectors ? = 4? + 6? − 8? and ? = 6? − 8? + 4? are added together describe the characteristics…

A: If two vectors ? = 4i+ 6j- 8k and ? = 6? − 8? + 4? ar

Q: a, b, c are non-zero vectors and a is perpendicular to both b and c. If |a|= 2, \b|= 3, |c|= 4 and…

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Q: Determine the value(s) of k such that the area of the parallelogram formed by the vectors a = (k +…

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Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=a and OT=b),…

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Q: Given the following vectors: u=(1, 2,-4) and v=(2, 3, 5) Find:

A: (a) The angle between the two vectors u and v is computed by the following formula. cosθ=u·v|u||v|…

Q: If a = (4, 3, 1, – 2), ß =(-2, 1; 2, 3) tween a and ß. are two vectors in V(R), find the angle be-

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Q: ±). 1.4 Use vectors to decide whether the triangle with vertices P(1,–3,–2), Q(2,0, –4) and R(6, –2,…

A: solution of the given problem is below ...

Q: If u, v and w are mutually perpendicular vectors, which of the following would not be true? O a) v•…

A: Given  vector u v and w are mutually perpendicular  .  ie .    u.v=v.w=u.w=0

Q: .If A = 2a, + a, - 3a, and B = 4ax + 2a, – 3a, are vectors, find (a) A· B (b) Á xB (c) Angle between…

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Q: Given the three vectors A = (3, 1, 1), B = (2, -1, 1), C = (0, 1, 2), find (AxB)xC %3D

A: The vector can be multiplied using the scalar product or dot product and vector product or cross…

Q: Under what conditions are the following true for vectors u and v in R2 or R3? (a) llu +vll = llull +…

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Q: If à = 2a, + 2a,y – a, and B = 3a, + 2a, – 6a, are vectors, find (a) Ả ·Ē (b) Ả × B (c) Angle…

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Q: Prove the property if a and b are vectors and m is a real number.a . b = b . a

A: Proof : let a and b are vectors and m is real number. To prove :   a . b= b . a

Q: Given three points P (1, 4, 6), Q (-2, 5, -1)  and R (1,  -1, 1) Find a vector perpendicular to the…

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Q: Find the magnitude of each of the two vectors a and b having the same magnitude such that the angle…

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Q: Given points: A = (4, 9, 1) B = (-2, 6, 3) C = (6, 3, -2) Using angles between located vectors,…

A: the given vertices are if the dot product of any two vectors is zero then we can say that A, B, and…

Q: Let ā = (1, – 5, 2) and b = ( – 1, 5, 3). %3D Find the angle between the vectors (in degrees).

A: We know that for two vectors a→ and b→,   cos(θ)=a⇀.b⇀|a||b|⇀⇀ where θ is the angle between vectors.…

Q: If the points with position vectors 10i+3j.12i-5j and ai+11j are collinear, Find the value of a.

A: The position vectors of the points which are collinear is: 10i+3j ,     12i-5j ,      ai+11j

Q: Given perpendicular vectors a = (5,3,-1) and 6=(2,2,k), find ||||.

A: Given perpendicular vectors a→=5, 3, -1,     b→=2, 2, k   To Find: b→

Q: If (a,ß.r) is a vector of magnitude 24 and having the same direction as the vector (1,-22,-2), then…

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Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated list…

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

Q: Given vectors a, b, c, such that a = 5c + 3d and b = 2c -d, 2a -3b in terms of c and d. express

A: Given vectors, a= 5c+3d b= 2c-d

Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated…

A: To determine the value of b.

Q: - Find the lengths of triangle ABC using vectors, knowing that: A (3,1), B (6,4), C (-1,3)

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

Q: In Figure , A, B, C, D,E , and F are the vertices of a regular hexagon centered at the origin.…

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Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated…

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Q: Given three vectors A, B, and C as follows, A = a, + a,2 – a 3, В 3 — а,4 + а,, С 3D а,5 — а,2, find…

A: Please see the explanation below

Q: Suppose that A, B, and C are vertices of a triangle and that a, b, and c are, respectively, the…

A: Let A=(x1,y1,z1)B=(x2,y2,z2)C=(x3,y3,z3)

Q: Let ā = (4, 3) and b = (– 4, 4). Find the angle between the vector, in degrees.

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Q: Given three vectors A, B, and C as follows, A = a, + a,2 – a,3, В %3D — а,4 + а,, С 3D а,5 — а,2,…

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Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 3. +-b and Aa…

A: We have to find the value of lambda by using the data given above

Q: Given points: A = (4, 9, 1) B = (-2, 6, 3) C = (6, 3, -2) Using norm of located vectors, prove that…

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Q: In Figure , A, B, C, D,E , and F are the vertices of a regular hexagon centered at the origin.…

A: Given that, OA→=aOB→=b

Q: Given the points P(4, 4, 3), P(1, 4,0) and P3(10,0, 2). Find the vector that is orthogonal…

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Q: Which polygon is the result of reflecting polygon 1 through AB, then translating the reflected…

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Q: In Figure , A, B, C, D,E , and F are the vertices of a regular hexagon centered at the origin.…

A: a=OA→  &  b=OB→

Q: If v and w are two nonzero vectors and θ is the smallest nonnegative angle between them, then v . w…

A: Given: If v and w are two nonzero vectors and θ is the smallest nonnegative angle between them, then…

Q: Given the triangle with vertices A=(1,2,3), B=(3,-1,0), and C=(4,1,2), find unit vector of BM, i.e.…

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Q: Given the three vectors A, B, and D, show that A (B +D) = (A · B) + (A · D).

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Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated…

A: It is known that any two vectors are orthogonal if their dot product is zero. The given vectors are…

Q: 6. Show that the points A, B and C with position vectors d = 32 – 4) – 4k, b = 2î – ĵ + k and & = î…

A: To show that the points A,B and C with a given position vectors forms a right angled triangle.

Q: The following are the vertices of a triangle A(4, 0, -1), B(-4, -1, 0), and C(3, 1, 1), find: vector…

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Q: Given the points A: (2,3,6) and B: (-3,-4,1), find the vector u = AB ū = < U

A: NOTE: Refresh your page if you can't see any equations. . here we have