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-

Q: The vectors u-(2,-1,1) and v= (1,1,2) in R3, the angle e between u and v is

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Q: If ū and i are two vectors, prove the identity ld + 레? + |d - 비? = 2| + 2|미2

A: This question is based on vector multiplication.

Q: |Given the vectors a = (1,2, 3) and b = (1, –1,2), what is the dot product a - b · a? 4 5 14 (7, 1,…

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

A: Given that P , Q & R lie on a straight line. It means vectors are coplanar . since if vectors…

Q: If v . w = 0, then the vectors v and w are________.

A: Lets two vector be v and w. v.w = v × w × cosθ Where theta is angle between v and w.

Q: If the vectors a=(2,5,-1) and b3(3,-3,k) are orthogonal, the the value of k is

A: Given : a = 2,5,-1b = 3,-3,k

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

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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: Find the measure of the angle between the two vectors. 5) u= (4, 9) v =(-6, -8) 6) u= (8, 5) v =…

A: To find - angle between u and v Use of - cosine formula of finding angle between vectors

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: 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: if vector AB=i+7j-4k and B is the point (9,3,5) find A

A: Let A=ai^+bj^+ck^B=di^+ej^+fk^ be twovectors.Then AB→=d-ai^+e-bj^+l-ck^

Q: Suppose thatu and v are vectors in both of length and that the length of u-v is and the angle…

A: Let's find.

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: Given that - (1, 2, 3) and - (4. 0, – 4) find the vector where %3!

A: In this question we have to find the vector z.

Q: If 7, r, and r, are three parallel vectors of the same magnitude Prove that i+r, +r, is equally…

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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: 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: Find 2?, −3?, ? + ?, and 3? − 4? for the given vectors ? and ?. ? = (−2, 4) , ? = (4, −2) 2u=____…

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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: If v.w 0, then the vectors v and w are

A: We know that two vectors u and v are said to be orthogonal if u . v = 0.

Q: Find all unit vectors perpendicular to (3,1,4) that make equal angles with j and k.

A: Here we have to find the all unit vectors perpendicular to (3,1,4) that make equal angles with j and…

Q: Given the points A: (1,6,3) and B: (2,-3,3), find the vector ü = AB %3D

A: To find- vector u.

Q: Let the vectors a=[1,1,0] b=[3,2,1], and c=[1,0,2]. Find the angle between а) а, b b) b, с с) а+с,…

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Q: Find a vector perpendicular to d = [5,–4,6] and h = [-1,3,9].

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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 and b are unit vectors in R', show that ||a x b||? + (a · b)² = 1. %3D

A: On solving this we will get:-

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 a = (−2, −5, −3) and b = (1, −4, 2), find 1.  5a − 1/3 b. 2. The length of a.

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Q: If the vectors a=(2,5,-1) and b=(3,-3,k) are orthogonal, the the value of k is

A: Given : a = 2,5,-1b = 3,-3,k

Q: The angle between the vectors a=(2,6) and b=(3,-1) is :إختر أحد الخيارات а. 4 b. С. 3 d. 2

A: The required angle is, option (b) π/2 The detailed solution is as follows below:

Q: 2. If A = 2a, + 0.3a, – 1.5a, and B = 10a, + 1.5a, - 7.5a,, Show that A and B are dependent vectors.

A: The solution is given as

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: - 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: 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: 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: and b are two unit vectors such that + 2b and 5 a. 4 b are perpendicular to each other, then the…

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Q: Since A, B and C vectors are perpendicular to each other, A, B, C, =? A -6) â, 1 (8) â, + A‚⸠B 19)…

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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: If u = (1,-3,2) and v = (-2,3,4). Find the distance between the vectors d(u, v) and d(v, u).

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Q: Given the vectors a = (−2, −5, −3) and b = (1, −4, 2), find A unit vector in the direction of a.

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Q: ) Find the cross product of the given vectors e = (6,-2,3) and f= (2,5,-1).

A: Given that  e= (6,-2,3) and f= (2,5,-1). We find vector cross product of this given vector.…

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

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Q: Show that for any two vectors u and v: = |

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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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