Let i and v be two orthogonal unit vectors in R³. We have a triangle ABC in IR³ such that AB = 2u – 6v, BỎ = ủ+7v, CÁ= -3ủ – v. Find the angles of the triangle ABC.

Q: Find the angle, to the nearest degree, between the vectors U and V U=4i+5j, V=7i−4j

A: Consider the given vectors U=4i+5j , V=7i-4j First, find the dot product of vectors of U and  V…

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 the vectors u = (-3, 1, 2), v = (1, 2, 1), and w = u + mv, determine the value of m so that…

A: The given vectors are u=-3,1,2,v=1,2,1 and w=u+mv. We have to find the value of m.

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: Find the angle between the vectors v and w in each of the following: (a) v= (4,1)T, w=(3,2)T (b)…

A: topic - angle between vectors

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 the angle between the diagonals of a parallelogram constructed on the vectors a=2 i +j and b=-2…

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Q: snip

A: We know that two vectors u and v are said to be orthogonal if their dot product u . v = 0. Given…

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

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Q: Given the vectors u=, v= find u+3v| 3. 15 -1

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Q: Find the positive value of m that makes the angle between the vectors equal to 5 a = i +j+k b = mi –…

A: Given that, a⇀=i^+j^+k^ b⇀=mi^-k^ Then we get, a⇀·b⇀=i^+j^+k^·mi^-k^a⇀·b⇀=m+0-1=m-1 Moreover we get,…

Q: given the vectors u = (2,4) y = (- 1,3) and w = (2, -3) Determine the values ​​of α and β such that…

A: Given vectors are  U = (2,4) so we can write it as=  2i + 4j ( i is the unit vector in x direction…

Q: given u=5i+j+(a+2)k  and v= (3b-1)j +4j+ 6k  determine a,b so that v are parallel vectors

A: Given that, u=5i+j+(a+2)k  and v= (3b-1)j +4j+ 6k  We have to determine a,b so that u and v are…

Q: Let a and y 6 Find the vectors v = 5x, u = x + ÿ, and w 5a + %3D || ||

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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: Given v = 2i + j, w = 6i + 3j, find projw v. Then decompose v into two vectors, v1 and v2, where v1…

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Q: If U and W are unit vectors in R" and |U - 3W = v13, then the angle between U and W is: O a. 30° O…

A: Option C will be the right answer.

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: . Given two vectors = w a = a2 show that

A: Given w→ = w1w2w3a→ = a1a2a3 We know that the cross product of w→ and a→ is w→×a→ = ijkw1w2w3a1a2a3=…

Q: Given vectors u and v below, find c such that u and v are orthogonal. u = [5, –5, c) v = [-3, 1, –1]…

A: If two vectors are orthogonal then their dot product will be zero

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

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Q: Find the angle between the two given vectors. u = (1, –4, 1), v = (0, 2, –2)

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Q: Given the vectors u = 2i+j and v = 4i-6j, find 4u and u-v. Write your answers in the form a i+bj. 4u…

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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: 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: 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: Given the unit vectors A, B, C,D that are in the same plane. The value of u-(AxB). (C.D)x(AxB).(C.D)…

A: Please see the explanation below

Q: Given v = i + 2j, w = 3i + 6j, find projw v. Then decompose v into two vectors, v1 and v2, where v1…

A: v=i+2j, w=3i+6j Now, v·w=i+2j·3i+6j=13+26=15 & w=32+62=45 Therefore,…

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

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Q: If v = a1i + b1.j and w = a2i + b2 j are vectors, the product v . w, called the________ , is defined…

A: If v=a1i^+b1j^ and w=a2i^+b2j^ are vectors, the product v.w, called the __________, is defined as…

Q: Find the value of a so that vectors U = ai + 6j and V 5= 9i + 12j are perpen dicular.

A: Our Aim is to find the value of a so that the vectors U=ai^+6j^ and V=9i^+12j^ are perpendicular.

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: The vectors a and bare unit vectors such that a a+b and 2a +jb are perpendicular. --Determine the…

A: The given vectors a→ and b→ are unit vectors such that a→.b→=12.Given: a→+b→ and 2a→+jb→ are…

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 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: 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: Given v = 3i - 2j, w = 2i + j, find projw v. Then decompose v into two vectors, v1 and v2, where v1…

A: Given that, The vectors  v = 3i - 2j, w = 2i + j. We have to find projw v By using a formula, projw…

Q: Find the angle between the vectors v and w v = (−2, 3, 1)T , w = (1, 2, 4)T

A: Consider the given vectors: Here the objective is to find the angle between vector v and w.

Q: Given the three vectors A = 3ix + 2iy – İz B = 3ix - 4iy – 5iz C= ix - İy + İz Find the following:…

A: We have to find the vector

Q: For the pair of vectors U = -2i + 8j, V = 2i + 8j, findU + V, U - V, and 4U + 5V. U + V = ( |)i+(…

A: We use the following formula to find the u+v: (ai+bj)+(ci+dj)=(a+c)i+(b+d)j

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: 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: Suppose that |u| = 6 and |v| = 9, and that u times v = -37. Find the angle θ between the vectors u…

A: Vector Question