Let ū and v be two orthogonal unit vectors in R. We have a triangle ABC in R such that AB = 2ū – 6v, BC = ü + 7v, CÁ= -3ū – v. Find the angles of the triangle ABC.

Q: Determine the angle between the given vectors. (а) а — 3і — 2ј, b %3 2i + 2j

A: a→=3i - 2jb→=2i + 2j

Q: Given vectors u=i+2j and v = 3i + yj, find y so that the angle between the vectors is 60°. roo…

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Q: Let u and v be two orthogonal unit vectors in R. We have a triangle ABC in R³ such that AB = 2ü –…

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Q: Find the value of a so that vectors U = ai + 3j and V = 9i + 9j are perpendicular. a =

A: Given: U=ai+3jV=9i+9jθ=90ο

Q: Find a vector v such that v = 15 and v is in the same direction as –li + 13j

A: The solution is given as

Q: If A = 6i + 7j – 10k, B = – 4i + 5j + 6k, C = 10, and C is perpendicular to both A and B, write the…

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Q: Find the angle θ between the vectors (a) in radians and (b) in degrees.

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Q: Find the area of the parallelogram that has the vectors u and v as adjacent sides, where ||u|| = 2,…

A: The area of the parallelogram is ∥u∥×∥v∥×sinθ=2×12×sinπ3=24×32=123   Here θ= the angle between u and…

Q: . Compute the dot product of the given vectors and find the angle between them: a) u = (3,7,-2) and…

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Q: Find the angles between given vectors. (a) ā = 3i + 4j and b= 5i – 4j (b) a = 3i +4j - 5k and 5= 6i…

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Q: Given vectors u = 2xi + 9j and v = xi - 4j, find x so that u and v are orthogonal.

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Q: Two non zero vectors a and b have respective magnitudes a and b , respectively. Given that c = a×b…

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Q: Given vectors ū = [3,2, –1] and v = [-2,2,4] , calculate the following: %3D %3D a) 2ū + 30 b) ū · v…

A: Use vector properties.

Q: Let i and v be two orthogonal unit vectors in R³. We have a triangle ABC in IR³ such that AB = 2u –…

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Q: Find the value of a so that vectors U = ai + 9j and V 3i + 12j are perpendicular. %D a =

A: Since, We know that Two Vectors are perpendicular to each other if and only if their dot product is…

Q: Find the value of b so that vectors U = 5i +12j and V = 4i + bj are perpendicular.

A: Given :          U=5i+12jV=4i+bj

Q: Let the cosine of the angle between the vectors p and q be à such that 2p + q = i + j and p + 2q =…

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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: Let i and v be two orthogonal unit vectors in R'. We have a triangle ABC in R such that AB = 2u –…

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Q: Find the angle 0 between the given vectors to the nearest tenth of a degree. U = 15i – 6j, V = 4i +…

A: Given, Vector U = 15i -6j        U = 152 +(-6)2 = 225+36 = 261 = 16.2 Vector V = 4i +13j         V =…

Q: A. Give the Cross products of the unit vectors (i, j, k).

A: Understanding of cross product of three vectors are required to under this.

Q: The vectors a, b and c are such that 2a – b+c= 0. If a = 4i – j+k and b = i- 2k , find a unit vector…

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Q: Find the angle between the vectors v and w v = (2, 1, 3)T , w = (6, 3, 9)T

A: We need to find the angle between the two vectors.

Q: Determine the angle between the given vectors. a = 3i – 2j, b = 2i + 2j (b) и %3D (1,—4, 2), v %3D…

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Q: Given the vectors →u=−6i−3j and v→= 10i+5j perform the operations below. →u+→v=____________ →u−→v=…

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Q: Find the angle between the vectors u = 2i − 3j + k, v = i − 2j + k (a) in radians and (b) in…

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Q: Find the angle between the vectors v and w v = (2,−3)T , w = (3, 2)T

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Q: Let x→=2i→−12j→+k→ and y→=12i→+2j→+3k→ be the two vectors. Find the angle (in radians) between the…

A: Given two vectors are To find angle between given two vectors.

Q: Given the vectors u = -i-5j and v =-3i+2j, find u v

A: Given vectors are  u=-i-5j     and   v=-3i+2j

Q: Use the vectors u = a1i + b1j, v = a2i + b2j, and w = a3i + b3j, to prove the given property : u . v…

A: Consider the following vectors: u→=a1i^+b1j^v→=a2i^+b2j^…

Q: If u, and uz are orthogonal unit vectors, and v = au, + bu2, find v•u . v•u1 II

A: topic - vectors

Q: Show that each pair of vectors is perpendicular.    i + j and i - j

A: Given: u=i+j ,v=i-j

Q: Let u = a1i + b1 j, v = a2 i + b2 j, w = a3 i + b3 j. Prove the given property by obtaining the…

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Q: Given vectors u and v below, find a such that u and v are orthogonal. [-20, –4] v = [a, –25] u = a =…

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Q: Find the angle between the vectors u = i − 2j + 2k and v = −3i + 6j + 2k.

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

Q: Find u * v if u and v are unit vectors and the angle between them is (2pi)/3

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Q: If u, and u2 are orthogonal unit vectors, and v = au, + bu2, find v•uq. = 'n.a v•u,

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Q: .Let u and v be two vectors with u x= 2 and 7-5=-2 Find the angle 0 between u and i

A: cross product of the vectors:A⇀×B ⇀= A⇀B⇀sinθn^  (It's a vector quantity.)A⇀×B ⇀ =  A⇀B⇀sinθDot…

Q: Let A and B be nonzero vectors and let C = ||B||A+ ||A||B . Show that the measure of the angle…

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Q: If a = 2i+j-k, b=-i+2k, and c=i+2j-2k, (i) Find a unit vector perpendicular to the plane of a and b.…

A: Let two vectors be defined as x=x1i+x2j+x3k and y=y1i+y2j+y3k . The dot product of the vectors, x ,…

Q: Show that if u+v and u – v are orthogonal, then the vectors u and v must have the same length. If 0…

A: As per our guidelines we are supposed to do only first question among multiple questions. To get the…

Q: The angle between the vectors ū = i + 2j – 4k and w = 2î + 3j + 5k is obtuse.

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Q: Find the angle between the vectors u = 3i + 2j + k, v = 2i − 3j (a) in radians and (b) in degrees.

A: Vector: u=3i+2j+k v=2i-3j u=<3,2,1> v=<2,-3,0>

Q: For the pair of vectors U = 9i + 4j, V = 5i + 5j, find U + V, U - V, and 4U + 5V. U + V = ( )i + (…

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Q: Two non zero vectors a and b have respective magnitudes a and b , respectively. Given that c = a × b…

A: To show that,

Q: the angles between the vectors u = 2i - 2j+ k, v = 3i + 4k = O 84.2 O 40.2 O 48.2 80.3

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Q: Calculate the angle 0 between vectors a and b when a = i – 2j + 2k , b = 2i + 3j + k %3D

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Q: Let u = a1i + b1 j, v = a2 i + b2 j, w = a3 i + b3 j. Prove the given property by obtaining the…

A: Given that, u=a1i+b1jv=a2i+b2jw=a3i+b3j

Q: Find the angle between the vectors u and v to a nearest degree: u = j + k, v = i + 2j – 3k

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