a b Consider the vector space W { : a %3D с d 3 let v = 4 -3 wo different ordered bases S and T for W. mine [v]s and [v]r•

Q: Let v1 = [1 2 3], v2 = [3 2 1], v3 = [2 1 3]. Find a vector in the Span{v1, v2} that is orthogonal…

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Q: Consider the vector Find two vectors W₁, W2 E R³ such that: • Both w₁ and we are orhogonal to v. •…

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Q: Find a vector b such that |b| = 1/2 that is parallel to a = but with opposite direction.

A: Given that: |b|=12a=<-6, 3, -2>

Q: Help

A: Step 1:Step 2: Step 3: Step 4:

Q: Find vector c × (a + 3b), where a, b, and c are given below. ijk i j k -1 a = 509,b=0 0 1 0 -9i+27i…

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Q: b. Find a specific vector u in V and a specific scalar c such that cu is not in V. Choose the…

A: Given that V=xy  ;x<0  and y>0

Q: Show whether R³ of the set B is a base and find the coordinate vector of the vector u = (- 1, -5,9).

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Q: Let V = R2, defined the addition by: (u1 +u2) + (V1 + v2)= (U1 +v1 , Uz +V2 + 1) With standard…

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Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

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Q: Let V1 = 1 v2 = V3 = and y = 4 Let W = span {V₁, V2, V3}. Find the orthogonal projection of the…

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Q: For any vector A,ix (i x A) +jx (j xA) + kx (k xA) = -2A ylan O İhi O

A: We use vector triple product to answer the given question.

Q: -3 3 Let u = -5 and i: 7 Find a vector w not in span {u, v}. 4 -3

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Q: Let vv be the set of all vectors of the form -a b vectors u and in R³ such that W = span{u, v}. ū =…

A: Given space W =

Q: f u = and v = v1, v2, v3 > are two vectors in 3-space show that u × v=    i j k u1 u2 u3 v1 v2 v3

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Q: Consider the points A (10, 9) and B (0, – 7). Find the vector AB. АВ

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Q: Use the triple scalar product to find the value of p that makes the three vectors below coplanar.…

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Q: A. B. | Find a nonzero vector w € R³ which is orthogonal to u but not orthogonal to v Find a nonzero…

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Q: find the derivative of (2³ + j)² O 23 +j O 223 + j O 625 + j6z² O 325 + j3z?

A: Derivative of (z3+j)2 is 2(z3+j)2-1(3z2+0) = 2(z3+j)×3z2 = 6z2(z3+j) = 6z5+j6z2

Q: Find a non-zero vector WER¹ which is orthogonal to all of the following vectors: V1 = Enter the…

A: Answer

Q: Write a in the form of a = a¡T + a„N at t = 0 without finding T and N for r(t) = (2 + t)i+ (t +…

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Q: Let å = (- 5, 5, – 3) and b = (4, – 1, 0). Find a unit vector which is orthogonal to å and b and has…

A: Given query is to find the unit vector orthogonal to a and b

Q: If A is a conutant vector and R= 3xi+ 3yj+ 32K, then grad (3A -R) = ? %3D A O 3A ©9A 27 A

A: A is a constant vector  R=3xi+3yj+3zk 3AR=9Axi+9Ayj+9Azk To find grad(3AR) Let Φ=9Ax+9Ay+9Az gradΦ=i…

Q: Determine the scalar triple product u (v x w) of the vectors u = i + 2j + 3k; v= -i-j+k; w = i+j+k…

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Q: Find the projection of the vector v onto the vector w if v = 2i + j and w = 6i + 3j

A: we have given v and w vectors . We have to find the projection of the vector v onto the vector w

Q: Which of these operators produces a scalar when it acts on a vector? A B D Ⓡ u. V V D2 V. Vx

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