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

Q: Find a unit vector that is orthogonal to both u = i − 4j + k and v = 2i + 3j.

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Q: C A

A: We use Triangle law

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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: Are the three vectors: Ū;=4i-8j+k,V=2i+ J-2K and Ūz =3 i-4 j+12K in the Same Plane?

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Q: Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.

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Q: What is the resultant of vectors a and b? ( A ) GL B

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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: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Determine the length of each vector.

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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.

Q: Find the value of  x  so that the two vectors  (27,1,13)  and   (x,0,1)  are orthogonal

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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: If v and w are two non zero vectors, the vector projection of v onto w is  projwv=v.ww2w Substitute…

Q: Show that Il all = 11b|l Are the vectors ã' and b equal?

A: ||a|| = ||b|| a and b are not equal.

Q: Find the vector v of length 6 that has the same direction as the unit vector (1/2, V3/2).

A: Consider the following values: magnitude=6unit vector=12i^+32j^

Q: Decompose V into in two vectors V1 and V2, where V1 is parallel to W and V2 is orthogonal W. V=2i+j…

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Q: Prove that if the vectors a,b parallel, then āxb=0. are %3|

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Q: Find the angle between the vectors u = /2i - 9j and v =v2i+j-2k.

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Q: When decomposing the vector into the sum of two vectors the first is parallel to the other vector…

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Q: Find two vectors of norm 1 that are orthogonal to the vectors u = and v =

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Q: 2.) Find two vectors that are orthogonal to the vector v = 8i - j

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

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Q: Decompose v into two vectors v, and v2, where v, is parallel to w and v, is orthogonal to w. v = 2i…

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Q: Determine m such that the two vectors are orthogonal.

A: The vectors 5mi^+3j^ & 2i^+7j^

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 of the given vectors and then we have to decompose v into two vectors, v1 and…

Q: Are the vectors v = 6i - 3j and w = i + 2j orthogonal?

A: Two vectors are considered to be orthogonal if their dot product is zero.

Q: Find a unit vector orthogonal to both u and v. u = 8i - 16j + 4k v = 16i + 32j – 12k

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Q: Is it possible to have ||u−v|| = ||u + v|| if u and v are nonzero vectors? Justify your conclusion…

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Q: Compute the distance between the vectors u = and

A: Given vectors are u=42−16 and v=4315. We have to find the distance between the vectors u→ and v→.…

Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

Q: Prove that the vectors v= and w= are orthogonal.

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Q: Show that v, = v 2 V2 3 span R and express the vector v= as a linear -7 %3D combination of v,,v2.

A: Solve the following

Q: Determine whether the vectors u= i + 5j − 2k,  v = 3i − j and w = 5i + 9j − 4k are coplanar

A: We have to determine whether the vectors u= i + 5j − 2k,  v = 3i − j and w = 5i + 9j − 4k are…

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 v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

A: Explanation: Given that,  Vectors v and w length is 3 angle between vectors v and w:…

Q: Find a unit vector orthogonal to both u and v. u = 31 - 2j - 5k V = +

A: Given: The given vectors are: u=3i-2j-5kv=12i-34j+110k To find: Unit vector orthogonal to both u and…

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: Determine whether the vectors AB and PQ are equal to each other.

A: Solution of the problem as follows

Q: Find three mutually orthogonal unit vectors in ℝ3 besides ±i, ±j, and ±k.

A: Vector: At first we can take a=<1,1,1> The second case we can take b=<0,1,-1> The…

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

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Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

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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: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

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

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Q: Find the values of ( x ) such that the vectors and are orthogonal.

A: Given: The two vectors are: 3,2,x and 2x,4,x Also, the two vectors are orthogonal.

Q: Are the vectors v = 2i + 3j and w = 6i - 4j orthogonal?

A: Are the vectors v = 2i + 3j and w = 6i - 4j orthogonal?

Q: Find two unit vectors that are orthogonal to both u = -7i+ 3j + k, and v= 2i + 4k

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Q: State whether the vectors are parallel, orthogonal, or neither. 5) v = 2i + j, w =i- 2j 6) v = 2i +…

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Q: Find a so that the vectors v = i- aj and w = 7i + 7j are orthogonal. ..... une on integer or o…

A: If two vector orthogonal then dot products will be zero