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

Q: If w = -2i + 6j, find the following vector: 2(-2) + 4(-6) W.

A: Given: The vector w=-2i^+6j^. w2 can be calculated as, w2=-22+622        =402       =2102…

Q: The following diagram shows the parallelogram ABCD. B A D Let AB =p and AC=q. Find each of the…

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Q: Given vectors v = (3, -1) and w = 1 (-4, 6), find 2v - 2W {8, -5) (4, -5) (-5, 4) (-8, 5) (-8, -5)

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

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Q: For what values of a and ß will the vector (a, 1, B) be orthogonal to (2, 0, 7) and (-1, 1, 2)? α =…

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Q: For the vector a,b,c ∈ IR3 a+b+c=0 and ===1 then ?

A: We will first assume a=(a_1,a_2,a_3),b=(b_1,b_2,b_3) and c=(c_1,c_2,c_3).Now will will use…

Q: For the pair of vectors, find U+V, U-V, and 3U-4V. U = , V = U+V = ? U-V = ? 3U-4V = ?

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Q: for what value of Ca) will the Vector ū = -41-8)4ak,ū =ei+4j-5k are parallel

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Q: B- For what values of a1 are the vectors [a1,4,3] and [3,-2,12] are 1) Orthogonal? 2) Parallel? 3)…

A: Angle between two vector

Q: If v=3w then the two vectors v and w are ................

A: Given :                    If v = 3w, then the two vectors  v and w are ____________

Q: For any three vectors a, b, and c, we have a x (b x c) (a x b) x c. اختر احدى الدجابات True False

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Q: 2 Describe each of the translations shown using column vectors. a d e 3 Using the vectors in…

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Q: Suppose that |u| = 10 and |v| = 7, and that u • v = -55. Find the angle θ between the vectors u and…

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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: What is the angle of vectors A=5m West and B=15m 60° North of West?

A: The vector A can be written as: a=-5i The vector B is 60 degree north of west that means it makes an…

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

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Q: If the angle between the vectors A = xâ, +â̟and B = /3â, +â, is 60°, find x.

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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: Given that the vectors a=(6,-1,2k)  and b=(-1,k+1,4) are perpendicular, what is the value of k?

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Q: For what values of c are the vectors and perpendicular?

A: we will use dot product of two vector.

Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b, 1/2a +…

A: answer

Q: 6. Given the following vectors, Draw: a) a-b b) 2c + a c) - (c-b) a X b of

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Q: Given the vectors à = and b =

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Q: Q1.If à = 2a, + 2a, – a, and B = 3ax + 2a, – 6a, are vectors, find (a) Ả · B (b) Ả× B (c) Angle…

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Q: If å = -î +ĵ b = 2î – 3j č = î - î And d = å – 3B + ¢ Determine the unit vector of d

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Q: 1. Assume the lengths of the vectors 2a – b and å + 35 , assuming å = (2,1,3) and b = (-1,2,2) 2. If…

A: Using scalar multiplication of vectors and magnitude of vector concepts  we can solve this question

Q: Given that the vectors ở = (1, 2– k,3) and b = (7, 4, k+2) are perpendicular, what is the value of…

A: Given vectors are: a→=1,2-k,3 and b→=7,4,k+2

Q: Suppose that u and V are vectors of lengths 2 and 3, respectively. If the angle between u and V is…

A: Dot product of two vectors u and v is given by

Q: Consider V=(6, -3) & W=(-4, 8) Find angle between the two vectors.

A: Recall: Angle between two vectors:     Let a→ and b→ be two vectors then,             cosθ=…

Q: For what values of b are the vectors (–88, 6, 7) and (b, b², b) orthogonal? Answer (separate with…

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Q: in the same sets of axis express the following vectors a=i+j, b=-1+j, c=a+b, d=2a,and e=a-b

A: The vectors are:-

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: For what values of ai are the vectors [a1,4,3] and [3,-2,12] are a) orthogonal? b) Parallel? c) Have…

A: This question is taken from the vector in which we have to find the value of a for the different…

Q: If A C =-8.4, A = 3i-4j, and C =6.5, the angle between the two vectors when they are drawn starting…

A: Let θ be the angle between the two vectors

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: For what values of a and B will the vector (a, 1, B) be orthogonal to (4, 0, 3) and (-1, 1, 2)? a =…

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Q: Given 2D vectors a and b such that |a|= 7 and |b| = 8 find the angle between the vectors if: a) |a…

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Q: Given that the angle between the vectors a and b is n/3, then the angle between the vectors -a and b…

A: Angle between two vectors a and b is π3 Let us find the angle between -a & b  Represented in a…

Q: Given vector A = 2а, + ба, За, and vector - B = – 3a, – 4a, – 5a,. Simplify the given mathematical…

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Q: For two vectors a and b, we always have a-b|<|a|-|b|. Select one: O True O False

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Q: For what values of a, b, and care the vectors (2a-b,a-2b,6) and (-2,2,a+b-2c) equal?

A: The given vectors are 2a-b,a-2b,6 and -2,2,a+b-2c . Note that, two vectors are equal if their…

Q: 14. Given that a and bare two vectors, then the vector (a + b) × (a – b) is A. perpendicular to (a –…

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Q: For the given vectors: å = (1,2),b = (-4,3) find: (a) 3å – 45 (b) à -5 (c) Angle between the vectors

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Q: Pls help ASAP. Pls show all work and steps.

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Q: For the pair of vectors, find U+V, U-V, and 2U-3V. U = , V = U+V = ? U-V = ? 2U-3V = ?

A: givenU=&lt;-3,0&gt;U=-3iV=&lt;0,2&gt;V=2jU+V=-3i+2jU+V=&lt;-3,2&gt;U-V=-3i-2jU-V=&lt;-3,-2&gt;

Q: If ả = 2ỉ + 33, b = j – ỉ and ở = 33 are vectors in 2D, then determine the of a + 3b + c

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Q: If the vectors in the figure satisfy Ju| = |v| = 1 and u + v + w = 0, what is |w|? u |w| =

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.