Find the vector, not with determinants, but by using properties of cross products. (i × j) × k

Q: find a vector b so that the equation A = b has infinitely many solutions?

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Q: Find the norm of and the unit vector ū in the direction of T if 5 3 = ||7| = 5, ||

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Q: find the value of k for which the vectors u and v are orthogonal.  u = 2i - kj v = 3i + 2j

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Q: Represent the vector with respect to each of the two bases { ] y = B = B2 =

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Q: The scalar product 0v is 0.

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Q: Find the coordinate vector[x],of x relative to the given basis B= {bl,., bn}. --]--[}]--[1] bị = ,b2

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Q: Consider four row vectors u, u, w, z of size 1 x n each and let a, bER Then. by multilinearity of…

A: The given statement is

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: 12. Let A = ( d ef g h Find the column vector B such that AB =

A: Let A be a square matrix. Use the following formulae, to obtain the required result.

Q: Determine the residual and Jacc - bian needed to solve the equation d²u 2u° = 0, - dx? 1 and u(1) 0,…

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Q: Let v = -7i - 7j-3 k and w =-3i+ 4j +6 k. Then the vector v – w can be written as

A: note : vector addition or subraction can be performed as  a⇀+b→ = (ax+bx,ay+by,az+bz) similarly for…

Q: Find the coordinate vector [x]g of x relative to the given basis B= {b, , b2}. 3 2 b, ,b2 2 -7 - 5

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Q: Write the projection of 2î +3j-k along the vector î+j.

A: Given that: 2i+3j-k along the vector i+j.

Q: products

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Q: Find the vector, not with determinants, but by using properties of cross products. (i x j) x k

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Q: Express the vector v =12i -5j as the sum of a vector parallel to b = 3i +4j and a vector orthogonal…

A: here we have to write the vector v in the form: v→=β1+β2Where β1 is parallel to b→ and β2 is…

Q: Find a vector parallel to the line of intersection of the planes x+ 3y – 2= =13, and 3x – 4y + = =-8…

A: Solution is here

Q: Find all values of the scalar k for which th e two vectors 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 the component of u = 2i + j − 3k that orthogonal to v = 3i – j, then verify your result.

A: This question can be solved using the concept of component of vectors.

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: Given vector u = (-1, –1) and v = (-1,1) , determine the value of 5v – u in component form.

A: A vector is a quantity with magnitude and direction. Given a coordinate system a vector can be…

Q: If the triple scalar product of the vectors A = i+ 3j + k, B = 2i -j-k and C= ai + 7j + 3k is zero ,…

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Q: Determine if the given vectors are orthogonal. a. v = 3i – 6j and w = 8i + 4j b. s = -2i – 5j and r…

A: Consider the pair of vectors  a)v=3i−6jw=8i+4j b)s=−2i−5jr=−4i+8j

Q: Find the cross product axb. 1+9k, b- 41-j+ 3k Verify that it is orthogonal to both a and b (a xb) (a…

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Q: Find the component form of the given vector. v = y 4 3 1 2 4 3.

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Q: Find the vector, not with determinants, but by using properties of cross products. k x (i - 2j)

A: The product of the vector helps to find the required product. The answer to the product is whereas…

Q: Express the vector - 4i - 8j + k as a product of its length and direction. - 4i - 8j + k=[Di+ ()j+…

A: To express the vector -4i-8j+k as a product of its length and direction.

Q: Find the vector x determined by the given coordinate vector [x]R and the given basis B. -4 [x] B% =…

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Q: "If u E R' is a nonzero vector, then there exists a vector v E R° so that the matrix A = (u v) has…

A: Given statement is true.

Q: Q2) Find the coordinate vector [x]B of x relative to the basis B={b1, b2} bị -31 X =

A: We are give: B = {b1,b2} where b1 =(-1, 2)T and  b2 =(-3, 5)T Also,  x1 =(-1, 3)T  We need to find x…

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: Find the vector x determined by the given coordinate vector [x]g and the given basis B. -2 B = ,…

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Q: find ||u|| for the given exercise, and give a unit vector in the direction of u.

A: The given vectors are, u=3-2   and   v=46 The objective is to find the norm of u and a unit vector…

Q: If possible, find scalars c1, c2, and c3 so that

A: Consider the equation: c112-3+c2-111+c3-14-1=2-23……1

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar -4w.

A: Given that : The vectors  u = 2i - 5j, v = -3i + 7j and w = -i - 6j .

Q: For any vectors U, V and scalars a, b, prove that (aU) x (6V) = ab(U × V) (a) (b) (aU) - (bV) = ab(U…

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Q: Find the volume of the parellepiped spanned by the three given vectors à, v and w (hint: use a…

A: The volume will be u.(v×w), the cross product will br applied be the determinant.

Q: Use the given vectors to find the specified scalar. u = 9i - 6j, v = -8i - 9j, w = -10i + 5j; Find u…

A: Given that     u = 9i - 6j , v = -8i - 9j , w = -10i + 5j Here we have to find u.(v+w)

Q: Q3. Find the cross product of the vectors and .

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Q: Find the length of the vector T

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Q: +0, then the matrix H = I – 2- vv7 is orthogonal and symmetric. Show that if the vector v

A: Given  H=I-2vvTvTv

Q: Determine "k" so that the vectors 3a- 4b and 5a+ 2k b are collinear. Justify your response.

A: Topic = Vector

Q: Express the resultant vector as a linear combination. f=-3i - 10j %3D g = 11i + 5j Find:-6f +2g

A: To find -6f+2g.

Q: a/(a + 3) x af а.) b.) (ā - 5)7

A: Recall if you can: Dot product of two vectors is a scalar A scalar times a vector is still a vector…

Q: Find the value of k for which the vectors -5 -1 4 and -4 k are orthogonal. k =

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

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Q: Find the addition of the vector using the component methods. 1. 9 m/s [N30°E] and 2 m/s [N 60°E].

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Q: For the two vectors a = 7i-4j+2k and b = -6i+3j-5k find the scalar component, compąb

A: Consider the formula for the scalar component. Find the dot product for a and b and magnitude of a.…

Q: find II u II for the given exercise, and give a unit vector in the direction of u.

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