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

Q: 27. Find a unit vector that is orthogonal to both i +j and i+ k.

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

A: topic:- vector algebra

Q: Decompose v into two vectors, v1 and V2, where v is parallel to w and v2 is orthogonal to w. v=i+j,…

A: A vector parallel to w can be obtained from the following formula, v1=v.ww2w and the other vector…

Q: For what value(s) of k are the vectors u = in R orthogonal? k v= -2

A: Here we have to find the value of k such that u=1k3 and v=k2-2-1 in ℝ3 orthogonal.

Q: 19 Use the given vectors to find V.w and V-V V= 6i-25, w=-4i-3

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Q: a) Find the value(s) of c for which the following vectors vị = ,v2 = --- 1 and v4 are linearly…

A: According to our guideline we are supposed answer only the first question if you want any particular…

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

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Q: H For the pair of vectors u = and v = in R*, find the size of the angle 0 between u and v. Hence,…

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Q: n Let ú and ú be two nonzero vectors in R" for which ú + 2v is orthogonal to ủ – 20. What is the…

A: We have to find the ratio

Q: 5. (a) Find two vectors of norm 1 that are orthogonal to the vectors u = (5) and pue (4 E)=

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Q: Consider the vectors 'v (1, 0, 1) and w (2,0, -2). %3D (a) Are 'v and w perpendicular? (b) Show that…

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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 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: 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: Given v = 7i+ 9j and w = - i+j, a. Find projwv. b. Decompose v into two vectors v, and v2, where v,…

A: Given that       v = 7i + 9j    and    w = -i + j Here we have to find projwv .

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: The vectors T and N, when defined, (a) are parallel. (b) are orthogonal. (c) have a zero cross…

A: T is the tangent vector and N is the normal vector.  So they are always orthogonal to each other.

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: Determine all vectors v that are orthogonal to u. (Set v, = t and v3 = s and solve for v2 in terms…

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Q: Q3. Prove that (only one): Ĝ = ax-ay is a unit vector? a- b- L = 6ax – 3a, + 2a, and M = 3a, + 2a, –…

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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: Two vectors in the plane, i & j, have the following properties: i · i = 1, i • j = 0, j • j = 1 a)…

A: Given data:- Two vectors in the plane, i and j have following properties; i·i=1, i·j=0, j·j=1

Q: 1 For what value(s) of h is the vector b = -3 in the span of the vectors V1 ,V2=

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Q: Find the possible values of x if vectors are j +2k, v =2i + j –- k and w = xi+j - k coplanar: u = i…

A: Given vectors are u=i-j+2k, v=2i+j-k and w=xi+j-k. To find the possible values of x if vectors are…

Q: Given vectors u = 1.3i + 4.8lj and v = -7.4i + 2j, u and v are: Parallel vectors. O None of these.…

A: Given vectors are u=1.31i+4.81j and v=-7.4i+2jTo check if the vectors are parallel they should…

Q: 14. Find a vector perpendicular to both of the vectors * (ũ + v) and (ũ – v) where ủ = 2i – j + k,…

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Q: Two vectors in the plane, i & j, have the following properties: i. i = 1, i .j = 0, j . j = 1 a) Is…

A: Given Properties of two vector i and j: i.i=1, (i is parallel to i )i.j=0 ,(i is perpendicular to…

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: 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: Consider the vectors y= 3i + 4j + 5k and w= i + j + k. Express the given vector in terms of i, j and…

A: The given vectors v=3i+4j+5k and w=i+j+k

Q: Find a unit vector orthogonal to the vector A= 2i-j+k and parallel to the vectors B= 2i+2j and C=…

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Q: R ABCDE is a pentagon. Let AB = u and AC = v E C D and AB = DC BD = 2AE AC = 2ED a) BD 3. Express…

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Q: V(PQ),V (PR), and V(PS) are 1. Find the volume of the parallelepiped PQRS if the vectors…

A: Solution of 1st question.

Q: 3. Find two unit vectors orthogonal to both j − k and i + j

A: We will find the two unit vectors orthogonal to j-k and I+j as following.

Q: Find a unit vector in the plane of the vectors A = i + 2j and B = j + 2k, perpendicular to the…

A: Consider the given question,

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: (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 angle between the vectors. 20 u= - 5 531-Si and v= zi-[2 V3= 2i:

A: The given vectors are

Q: B. Find the value of the constant ß such that the vectors: u = ßi + 11j – 3k and 2ßi – Bj – 5k, are…

A: See the attachment. Send your feedback.

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

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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: b/Let u and v be a nonzero vectors in 3- space, and let e be the angle between these vectors when…

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Q: Given v = 7i+9j and w = -i+j, a. Find projwv. b. Decompose v into two vectors v, and v2, where v, is…

A: Here we have to find projection  And decompose v in two vectors

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

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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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