For the vectors u=i+6j+ 8k and v = 10i – 3j + k, calculate projyu and scal,u.

Q: Find the unit vector in the direction of .

A: Given points are: P1≡32,72P2≡82,22 Then we get, P2-P1=82-32,22-72⇒P2-P1=52,-52

Q: For the pair of vectors, find U + V, UV, and 3U - 4V. U = (-7, 0), V = (0,5) U + V = U-V= 3U - 4V =

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Q: For the pair of vectors, find U + V, U-V, and 3U - 4V U = (4,1) V =(-6,3

A: Given that  U = (4,1) V =(-6,3) To find U + V, U-V, and 3U - 4V

Q: Find the angle 0 between the vectors. u = (2, 2), v = (4, -4)

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Q: 2. For the vectors u = -5i + k and v = 3j - 4k, find a. (u · v)u b. u - 3v

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Q: For any vectors U and V, show that |U x V]? + |U• V]? = |U°|V[?

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Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: v=2i+4j  and  w=-3i+6j. Now, v·w=2i+4j·-3i+6j=2-3+46=-6+24=18 & w=-32+62=45=35 Therefore,…

Q: Use the vector u= -1i -4j , v= -9i + 7j and w= 7i + 1j to find the following. u+ (v- w) = %3D i+ j.

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Q: find "a" so that the vectors v=i-ja and w=2i+3j are orthaganal?

A: Given,  v=i-ja and w=2i+3j Two vectors are orthogonal if and only if their dot product is zero

Q: Show which of the following are orthogonal vectors v, = 18] V2 = %3D Or = Liel Uz = 18

A: Check the dot product of given vectors are zero or not, if zero the orthogonal otherwise not

Q: Find the angle between the vectors u = (1, −1) and v = (0, 1).

A: Given query is to find the angle between the vectors.

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

Q: Find the angle 0 between vectors u = 2i - jand v = 6i + 4j.

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Q: Find the cosine of the angle between the vectors P1 (x) = 1 + 2x – x² and p2 (x) = 2 – 3x – 2x² with…

A: We have to solve given problem:

Q: For any vectors U and V, show that |U x V/? + |U · V[? = |U|°|V[? %3D

A: 1) The dot product of two vectors: a→·b→=a→b→cosθ 2) The cross product of two vectors:…

Q: photo attached

A: Given,

Q: For the pair of vectors, find U + V, U – V, and 4U + 2V. U = -5i + 6j, V = 5i + 6j

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Q: For any two vectors ū and i, ||ū + u|| = ||ū|| +||7||-

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Q: For any vector v in ℝ3, explain why v × v = 0.

A: Given v∈R3 v×v=0

Q: For the vector, find 2 -V, and 4V. V = 2i + 8j Your answ -v =-2i – 4j 4V = = 8i + 32j II

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Q: Find the angle between the two vectors u 2i+ j-7k and v =i-j+ 4k

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Q: Consider the vectors: u=(-2,6), v=(-3, –4), w =i+9j, and x=8i-6j.

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Q: 1. For the vectors u = 4i – j+4k and v= -i- 2j+3k, calculate the following: а) иху b) Vxu c) ux v

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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: Find a so that the vectors V=i-aj and w=2i+3j are orthogonal

A: Two vectors V and W are said to be orthogonal if their dot product is 0.    V.W = 0

Q: photo attached

A: Given,

Q: For the vectors u=i+6j+2k and v = 2i - 2j + 5k, calculate projyu and scal, u. proj, u= (Di+ Oi+ (Dk…

A: Given : u = i+6j+2k v = 2i-2j+5k

Q: Find a vector w perpendicular to both vectors u=2i-j+2k and v=3j-4k w=i+2j-3k w=-2i+8j+6k…

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Q: For two nonzero vectors u and v, if u v=0 then u and v are parallel.

A: Given that u and v are two nonzero vectors   Dot product of two nonzero vectors u.v=|u|.|v|…

Q: For the pair of vectors, find 3U- 4V. U = (3, 2), V= (-4, 3)

A: We have to find 3U - 4V

Q: Find the angle between the vectors u = (2, 5) amd v =

A: Given: There are two vectors: u=2,5v=4,-3 To determine: The angle between the given two vectors.…

Q: If U1 and U2 are orthogonal unit vectors and V = aU1 +b U2, find V.U.

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Q: Find two unit vectors that are perpendicular to both j + 2k and i – 2j + 3k.

A: Given that a→=j+2k,  b→=i-2j+3k   We know that the cross product of two vector is perpendicular to…

Q: 27-j+4k sī +2j-2k.

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Q: Find the angle θ between the two vectors.u = (1, −1), v = (0, 1)

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Q: For the vectors u = (- 1,3) and v= (-4,2), calculate proj,u and scal,u. proj, u = D

A: Vector and scalar projection

Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (1, 1) V =

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Q: Find the angle θ between the vectors.u = (−4, 1), v = (5, 0)

A: u = (−4, 1), v = (5, 0)

Q: (3) Find the angle between the vectors u= 2i-2j4tk and

A: given vectors are  u=2i-2j+k  and v=3i+4k find the angle between these vectors

Q: Consider the vectors x1 = (2, 1)T and x2 = (6, 3)T . Determine the length of each vector.

A: Given: x1=2i+j, x2=6i+3j we know that for any given vector v=ai+bj, length l of vector is given by…

Q: For the pair of vectors, find U+V, U-V, and 4U-2V. U = -9i+4j, V = 9i+4j U+V = ? U-V = ? 4U+2V =…

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Q: Find the angel between the vectors u and v if u=-4i+2j and v=3i+2j Round answer to two decimal…

A: Consider the dot product of two vectors.

Q: Find the cross products uxv and vxu for the the vectors u=2i-j-2k and v= i +3j-2k.

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Q: Find the following for the vectors u = 6i + 9j + v2k and v = - 6i – 9j – V2 k. a. v•u, v, and u b.…

A: We have to solve

Q: Use the points P(3, 1) and Q(7, 1) to find position vectors equal to PQ and QP.

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Q: Find the angle a between the vectors 3 a || -1 -2 - and 1

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