If V1= 2 i+ 10 j-11 k , and u= 2 i+2 j+ k, then, the value of the vector dot product (V1.V2) equals to 15? And the vector projv u is 0.1166 i+ 0.583 j- 0.641 k? * O TRUE False

Q: (3) Suppose a vector x is orthogonal to vectors u and v. Show that x is orthogonal to u+v.

A: We will use the fact that x is orthogonal to u and v to prove that x is orthogonal to u+v also

Q: Find a non-zero vector 7 perpendicular to the vector u 12 [3]. -6

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Q: Find a unit vector that is orthogonal to both u = (2, – 10, 8) and v = (4, 6, – 8).

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Q: The norm of the vector u = (1, 2, 3, 4) is 30. True O False

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Q: If vector u=2i+3j+4k is orthogonal to vector v=3i+2j-bk, then value of b is 4 1 2 3

A: Two vectors x , y  are orthogonal or perpendicular if x·y=0

Q: Find the vector component of u = ⟨5, 10⟩ that is orthogonal to v = ⟨4, 3⟩, given that…

A: Given,      w1 = projvu = ⟨8, 6⟩   and     u = ⟨5, 10⟩ = w1 + w2.      Where,  u = ⟨5, 10⟩ ,  v =…

Q: Why are there no vectors u and v in R,, such that ||u.||= 2, ||v|| = 3, and    uxv= -7?

A: The given values are, u=2, v=3,   and  u×v=-7. The objective is to find the valid reason for the…

Q: The value of the chiral vector of SWNTs if the n=8 , m=6 and the first vector length equal n/2+1 and…

A: Given that m=6,n=8to find the chiral vector of SWNT.  As we know that, the chiral vector c can be…

Q: Find the magnitude of vector u = 4i - 3j - 5k and simplify. O 2v3 O 3v2 None of these. 4 O 5/2

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 8 -x + 3y + z = 9 2. Find the normal vector,…

A: Find your answer below

Q: Refer to the vectors u, to ug. -5 1 1, u2 = u3 = U4 = -5 U5 4 4 Compute projs u8, where s = span{u5,…

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Q: Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector 10i – 2j +…

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Q: 4. Find two unit vectors orthogonal to both j-k and i+j.

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Q: Find all value(s) of t such that the vectors 2t i – 2 j– k and 2ti+ 3t j – 2k are nernendicular

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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 magnitude of u xv and the unit vector u= 5i - 5i - 3k, v= 0 O A. 0; 5i - 5i - 3k O B. V59;…

A: Here we have, u=5i-5j-3k and v=0 We have to find the magnitude of u×v and the unit vector parallel…

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

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Q: d) Prove that ||vxw||²+|v-w[? = ||v||²|w||² for all vectors v, w in R3

A: Prove the following

Q: If u and v are vectors in R^n, and if v≠0 ⃗, then u can be expressed in exactly one way in the form…

A: first draw a figure as below

Q: 1. The vector in the opposite direction to u = = (-1,0) and of half its length is

A: Explanation: Given that,  Vector u=-1,0 find the length of this vector  length of vector u =…

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: To Determine: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w…

Q: Find the vector ū which satisfies the given conditions. i =, Ju| = 2 , ū and i have opposite…

A: The unit vector,  , in the direction of the vector is calculated as follows.

Q: Find a non-zero vector & perpendicular to the vectors v = x = ► 3 H and u = 4

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Q: Dados los vectores u=2i-3j+4k y v=(4,1,-2) , calcular la norma (módulo) del vector u - 2v V37

A: Given: u=2i-3j+4k v=4,1,-2

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: the component of vector a are ax=2.0 units and ay=3.0units while that of another vector b are Bx=…

A: Given components of two vectors: Components of a are: ax=2.0 units and ay=3.0 units, Components of b…

Q: If the vector u = 2i-3j+v3k , then the length of u is -v2 True O False

A: # we are entitled to solve one question at a time , please resubmit the other question if you wish…

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 unit vector orthogonal to both u and v. u = 3i + 5j + 2k 1 + -k % = 2 4 10

A: We have to find the vector

Q: 7 Consider the vectors: U = 1 v = w = -2 2 Express W as a linear combination au + bv. What is b'?

A: WRITE  W AS A LINEAR COMBINATION OF U AND V ie. w = au + bv Using Row Elementary Transformation,

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: 1. For what value of c is the vector v = = (2,–5, c) orthogonal to w = (3, 2,9)?

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you.  If…

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. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

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Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: 1 Find two vectors of norm 1 that are orthogonal to the vectors u = and v = 3

A: Given problem is :

Q: 3. Find two unit vectors that are orthogonal to both j +2k and į -2j + 3k.

A: Solution is here

Q: 9. Show that for any real numbers a and b the vectors u = ai and v = bj are orthogonal?

A: Topic:-  vector algebra

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: Q3/ Show that the vectors (2i + 3j + 6k), (3i – 6j + 2k)and (6i + 2j + 3k) Are mutually…

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Q: 10. Let the vector v = 2i -3j + k, and the vector w = = -i+3j+ 2k. Find v x w.

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Q: (2) Given the vectors - -- -- --- 1 V1 = V2 = V3 = and w = are there scalars a, b, and c such that…

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Q: Determine whether the vector U = 2 is a linear combination of the vectors Xi = 2 X2 = and X ? Give…

A: Let  U→=aX1→+bX2→+cX3→  Where, a,b and c are scalar. Then,…

Q: A n = i-j+3k, n2 = 2i +j+ 3k to the two vectors.

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Q: Q3. Prove that (only one): ax-V3ay a- is a unit vector? b- A = 6ax – 3a, + 2a, and B = 3ax + 2a,y –…

A: Given two statements . We need to prove only one out of that  So, here we will prove first statement…

Q: 98 25) Gvon vectors v= 30tj and w=-2i -j. Decompose v into two vectors V, and Vz, where V, is…

A:

Q: Find the best approximation to z by vectors of the form cv1 + ¢2V2. 3 1 -7 -1 1 V1 V2 -3 3

A: To find  The best approximation to z by vectors of the form c1v1+c2v2.

Q: Find a unit vector that is orthogonal to both u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩.

A: The given vectors are u = ⟨2, −10, 8⟩ and v = ⟨4, 6, −8⟩. Compute the cross product of u and v as…

Q: O Are the three vectors: V= 4i-8j+kV= 2i+j-2k and ū;=3i-4j+12K in the Same Plane?

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Q: If i • ( or v• (u x w) or w • (u x 7) equal to zero, then the 3, and w vectors u. are coplanar.…

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Q: When decomposing the vector into the sum of two vectors, the first is parallel to the vector A = 2i…

A:

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