Find a non-zero vector a perpendicular to the vectors [3] and ū = 2 1

Q: 9

A: We need to determine all the values of the constant a for which the vectors

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

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Q: 2 Write the vector x= as a linear combination of the vectors -1 1) u=0 |, v=| 1 w= 1 1 N O H O O

A: Consider x = au+bv+cw then 20-1 = a100+b110+c11120-1 = a+b+cb+cc On comparing the coefficients , we…

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: Determine the constant a so that the vector i = (2x + 3y)î + (2y – 2z)j+ (x + 2az)k is a solenoidal.

A: Given : The vector v→ = (2x + 3y) i^ + (2y - 2z) j^ + (x + 2az) k^.   To determine the constant a so…

Q: Find two linearly independent vectors perpendicular to the vector 1 3

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Q: Find a unit vector orthogonal to both u and v. u = 3i + 5j + 2k V= 위해 + -k 10

A: Given the vectors u→=3i→+5j→+2k→, v→=12i→-34j→+110k→. To find: A unit vector orthogonal to both u→…

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

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Q: Find a non-zero vector v perpendicular to the vector u = [ -1 ]                          [ 8 ]

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Q: Q4) The vector product of two vectors is scalar product. F O T

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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: Let v = 2i - 5j and w = i - j.Decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

A: v=2i-5j  and  w=i-j. Now, v·w=2i-5j·i-j=21+-5-1=2+5=7 & w=12+-12=2

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: 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 vector v = 1 and the vector "function" w(k) = 1 For what value of k are i and w(k)…

A: Two vectors v→ and w→ are said to be orthogonal if v→·w→=0 Given v→=111w→=11k

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 all vectors in R* that are orthogonal to both 1 1 V1 = and V2 2 -2

A: Linear Algebra: The vectors are: v1=112-2v2=2112Let denote the vector v3=v1v2v3v4

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

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Q: Write the vector x=0 as a linear combination of the vectors u=0, v= 1, w= 1 1

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

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Q: Find two linearly independent vectors perpendicular to the vector V = 3 -5

A: Let's find.

Q: Find a vector orthogonal to both given vectors u and v . u=2i-3j +k  v= -3i +4 j +4k

A: Given, u=2i-3j +k  v= -3i +4 j +4k    We have to find the orthogonal vector to both given vectors u…

Q: Find two linearly independent vectors perpendicular to the vector 4 v =

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Q: 2. Express the vector v = 3i – 4j as the sum of a vector parallel to b = 2i +3j and a vector…

A: Given, v→=3i^-4j^ The parallel vector c→ to the vector b→=2i^+3j^ can be written as c→=λb→=2λi^+3λj^…

Q: Find a vector in the plane parallel to the line ax + by = c.

A: We know that, Slope of parallel lines are equal Given equation of line is ax + by = c Slope of this…

Q: Find a non-zero vector i perpendicular to the vector i

A: See the attachment

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: The orthogonal projection of the vector v =3i-j+k on the vector b 2i-j+k is

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Q: Let v = 2i - 5j and w = i - j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: Given vectors are: v = 2i - 5j and w = i - j The formula for the vector projection is given by…

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

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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 a unit vector perpendicular to i-j and to i +k and with a positive k component.

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Q: Find a unit vector orthogonal to both u and v. u = 3i – 5j + 2k -k + 10 - V =

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Q: Show that the vectors v1, V2, and v3 are linearly dependent, where n- . -. 3 V2 = 5 and v3 = 6 Vi =…

A: The given vectors are v1=12, v2=34 and v3=56

Q: Find a non-zero vector 7 perpendicular to the vector u = 5= [8]. 6

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Q: Find the vector projection of vector u onto vector v, and find the vector component of u orthogonal…

A: The projection of vector u onto v is given by projvu=u⇀v⇀v⇀2v⇀

Q: Find x if the vectors a =i+j+ 2k;b = xi-j+k; coplanar or linearly dependent.

A: Given,       a=i+j+2kb=xi-j+kc=3i-2j-k

Q: Find a unit vector orthogonal to both u and v. u = -3i + 5j + 2k V + 1k 10

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

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Q: Find a non-zero vector u perpendicular to the vector u =

A: If  A non zero vector is perpendicular to anather vector then their dot product is equal to zero.

Q: Find a unit vector orthogonal to both u and v. u = 2i – 5j + 3k 1 V = -k + 10

A: Please go through the attached solution. I hope that it  will help you .Thankyou . Best regards.

Q: For any vectorV and unit vector U parallel to V , then D-

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

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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: Find a vector 2 units long in the direction of v = 4i - j + 4k.

A: First find a unit vector in the direction of v = 4i - j + 4k.

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: Find two linearly independent vectors perpendicular to the vector i = |3

A: to find linearly independent vector perpendicular to vector v→=139 solution let X=x1x2x3 as we know,…