The vectors (i + j) , (i – j) and (k – i) are Parallel to each other A. Perpendicular to each other В. Oc. Coplanar None of These OD.

Q: Let A and B be nonzero vectors. Find k e R such that A – kB is orthogonal to A + B.

A: We know if a vector P→ is orthogonal to another vector Q→ then scalar product (dot product) is zero.…

Q: Find the angle between the vectors. (First: v = -21 exact u = i- 6j + k, approximate xx x +

A: topic:- vector algebra

Q: Given the vectors in parts a) and b), determine whether u, v, and w lie in the same plane when…

A: We have to determine whether vectors u, v and w lie in the same plane when positioned so that their…

Q: Find ||e − 4f||, assuming that e and f are unit vectors such that ||e + f|| = √3.

A: The step-by-step solution to the given question is ..  we have ,  e+f=3..........(1) we have to find…

Q: 3. Find the angles between the vectors: u = 2i + j, u = 2i – 2j + k, v = 3i + 4k a. v = i + 2j – k…

A: a.)u=2i+j , v=i+2j-klet θ be the angle between the…

Q: Which of the following vectors are equal to j × i? i × j

A: The standard unit vectors in three dimensions, i^, j^, and k^ are length one vectors that point…

Q: The vector sum v1i + v2 j is a ________ ________ of the vectors i and j, and the scalars v1 and…

A: The vector sum v1i + v2 j is a linear combination of the vectors i and j, and the scalars v1 and v2…

Q: Find all value(s) of t such that the vectors 2t i – 2 j– k and 2ti+ 3t j – 2k are nernendicular

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Q: 3. Find the angles between the vectors: u = 2i + j, v= i + 2j – k а. b. u = 2i – 2j + k, v = 3i + 4k

A: Angle between two vectors, θ=cos-1u→.v→|u→| |v|→ a)  u→.v→=2i+j.i+2j-k       =2+2 u→.v→=4 |u→|=22+12…

Q: Decompose the vector v=3i+2j into two vectors v1 and v2, where v1 is parallel to w=2i+j, and v2 is…

A: Decompose v into two vectors v1 and v2,where v1 is parallel to w and v2 is orthogonal to w.v=3i+2j,…

Q: Find the following for the vectors u = - 5i + 8j + V5 k and v = 5i – 8j – /5 k. a. v•u, v, and Ju b.…

A: As per Bartleby answering guidelines if a questions has multiple subparts then an expert is expected…

Q: Given v = 2i + 4j, w = -3i + 6j, find projw v. Then decompose v into two vectors, v1 and v2, where…

A: *The given vector v is, v=2i+4j *The vector w is, w=-3i+6j The projection of the vector on the other…

Q: (b) y =u°+In(2u), where u = e 4. Consider the vectors u,v and w are defined as u = -i+2j+2k, v =…

A: 4. Given the vectors u , v , w.

Q: Decompose v into two vectors,one parallel to w and the other orthogonal to w. v = 2i + j; w =4i + 3j

A: we have to decompose v into two vectors, one parallel to w and the other orthogonal to w. v = 2i +…

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

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Q: Find the angle between the following vectors relative to the Euclidean inner product on ℝ2. a.…

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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: Q2] (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

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Q: Find the following for the vectors u = - 6i + 7j + V2k and v = 6i – 7j - v2k. a. v•u, v, and u b.…

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Q: Find b so that the vectors v = i + jand w = i + bj are orthogonal.

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Q: Given v = - 3i + 5j and w = i+j, a. Find projwv. b. Decompose v into two vectors V1 and V2, where V1…

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

Q: Given v = - 7i + 5j and w= -i+j, a. Find projwv. b. Decompose v into two vectors v, and v2, where v,…

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Q: Find the vectors T, N, B at the given point where 0sts 2n. (1 3/3 8' r(t) =

A: We want to find the unit tangent vector , normal vector and Binormal vector

Q: Which of the following vectors are equal to j × i?(a) i × k

A: We know that, i×j=k Therefore, j×i=-k Hence the answer.

Q: Find a unit vector orthogonal to A in the plane of B and C if A = 2i - j + k, B = i + 2j + k, and C…

A: The given details are as follows.

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

A: we have to find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

Q: The area of the parallelogram whose adjacent sides are the vectors u and v is a) Ju · v| c) Ju x v|…

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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: Find the area of the triangle with two sides given by the vectors a = i – j+ 4k, and b = 2i – 4j+1k

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Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a –…

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Q: b) Find the value(s) of z such that the angle between the vectors U₁ = and U₂ = is equal to 30°.

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Q: Let v = 2i + 4j and w = -2i + 6j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: v=2i+4j  &  w=-2i+6j Now, v·w=2-2+46=20 & w=-22+62=40 Now,…

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: Given the vector u (2, 2), find the magnitude and - angle in which the vector points (measured…

A: Given that: u→=2,-2. Therefore, magnitude of the vector is= u→=22+-22=22.

Q: 10. In the diagram, M is the mid-point of CD, BP:PM = 2:1, AB AD = z. = x, and AC = y and %3D…

A: Given that:                               NOTE: As per our answering guidelines, we can only answer…

Q: If a = i+ 8j + k and b = i+ 13j + k, find a unit vector with positive first coordinate orthogonal to…

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Q: (b) Find a vector i that is parallel to ↑ and perpendicular to L.

A: As per your demand, we solve part b) only

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 cosine of the angle between the vectors P1(x) = 1 + 2x – x² and p2(x) = -1 – 3x + 2r² with…

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Q: (1b) Find vectors v and w such that v is parallel to y, w is perpendicular to y, and x = v+ w.

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Q: (1b) Find vectors v and w such that v is parallel to y, w is perpendicular to y, and x = v + w.

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Q: Find the following for the vectors v = - 9i + j and u = - 5i + V3j. a. v•u, Įv], and |u| b. the…

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Q: Find the following for the vectors u = - 9 i-2j + v2 k and v = 9 i+2 j- v2 k. a. v•u, v|, and u b.…

A: Let a→ = a1i^ + b1j^ + c1k^ and b→ = a2i^ + b2j^ + c2k^ two vector. Then, a.b = a1a2 + b1b2+c1c2 a…

Q: For the non-zero vectors A and B to be perpendicular to each other, the necessary and sufficient…

A: Given, For the non-zero vectors A and B to be perpendicular to each other, the necessary and…

Q: perpendicular to the plane formed by the vectors w1 = [1 2 1] and w2 = [2 2 3], with the z axis

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Q: Given the vectors v=i+3j w = 4i - j

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Q: If a = i+ 4j + k and b = i + 8j + k, find a unit vector with positive first coordinate orthogonal to…

A: Given : a=i+4j+k and b=i+8j+k.

Q: If v = 5i + 6j and w = 10i + 12j, find proj,v. Then decompose v into two vectors v, and v2, where v,…

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