Find the vector z, given that u = (5, -6, 2), v = (0, 2, 1), and w = (-6, W%3D 1. z = -u + 5v + w 2

Q: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩     (1/3)z − 3u = w

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Q: Find the vector z, given that u = (3, -2, 5), v = (0, 2, 1), and w = Z= z = −u + 4v + 1 _W 2 (-6,…

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Q: Find the vector with the given length || v || = 3, and in the direction of u = (0,2,1, -1)

A: Sol

Q: Given the vectors u = (-3, 1, 2), v = (1, 2, 1), and w = u + mv, determine the value of m so that…

A: The given vectors are u=-3,1,2,v=1,2,1 and w=u+mv. We have to find the value of m.

Q: Find the vector z, given that u = ⟨5, −2, 3⟩, v = ⟨0, 2, 1⟩, and w = ⟨−6, −6, 2⟩.   u − v + w − 2z =…

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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: Find a vector orthogonal to both v and u. V = 2i - 2j + k, u = -4i - 4j + 5k -6i - 7j + 7k 6i + 7j +…

A: Given is           v = 2i -2j +k           u = -4i-4j +5k         two vector a & b said to be…

Q: Find the vector z, given that u = ⟨5, −2, 3⟩, v = ⟨0, 2, 1⟩, and w = ⟨−6, −6, 2⟩. .   z = −u + 3v +…

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Q: Given the vectors u = (2, -2, 3) and v = (-3, 2, – 1), calculate the vector projection of u onto v…

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Q: (d) Suppose the three vectors x, y, z E R³ are known to be linearly independent. Are the three…

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Q: Find the initial point A of the vector that is equivalent to (3,7), and whose terminal point is…

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Q: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

A: Given: Find a vector that is orthogonal to v =〈1, 2, 1〉 but not to w =〈1, 0, -1〉

Q: Consider the points P(3, x, -2) and Q(5, 3, 4) in R3 . Find x so that the vector from P to Q is…

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Q: Find the vector z, given that u- (9, 2, 7), 2,-1), andw = 0,-4

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Q: Find the vector z, given that u = , v = , and w = . z = 8u - 3V - -W 2 1. Z =

A: We have been given the vectors  u = <1, 2, 3> v = <2, 2, -1> w = <4, 0, -4>

Q: Find the magnitude of the given vector. (-1, 2, 2)

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Q: If y is orthogonal to the vectors u and v, then y is orthogonal to u+ 3v. True False

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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: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩.     z = 5u − 3v −…

A: Given: u=1,2,3, v=2,2,-1, w=4,0,-4 for finding given vector z, we use given values

Q: Consider the vector v = (−1, 3, 0, 4). Find u such that (a) u has the same direction as v and…

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Q: Find the magnitude of the vector AB A=(4, 1) and B=(-3,0)

A: Given that, A = (4, 1) B = (-3, 0) We have to find the magnitude of the vector AB.

Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

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Q: Determine R21, the vector from P2(5, 2,–4) to P1 (3, –1,0). 2аx + Зау — 4а, — 2ах — Зау + 4a, | 4ах…

A: Given the points P25,2,-4 and P13,-1,0. To find vector R21 from above two points. The vector from…

Q: Find the component form of the vector v given ||v|| = 12 following the direction of u (3, –5)

A: Find the component form of the vector v given ||v|| =12 following the direction of u = (3,-5)

Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

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

Q: Find a vector orthogonal to both v and W. v = 3i + 2j + k, w = -5i - 5j - k 3i - 2j - 5k -3i + 2j -…

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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: Find the coordinate vector of w relative to the basis S = { u1, u2} for R u 1 = (4, – 4), u 2 = (4,…

A: Given: u1=4,-4u2=4,4w=0,24

Q: Find the component form of the vector v given ||v|| 12 following the direction of u (3, –5) %3D

A: The vector v in direction of u can be found  blew step.

Q: Find the vector z, given that u = (3, 2, 9), v = (2, 2, -1), and w = (4, 0, -4). %3= z = u - v + 2w

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( 5 , −…

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Q: Find two vectors in opposite directions that are orthogonal to the vector        u = ⟨3, 1, −2⟩

A: u=3, 1, -2 Let v=a, b, c be the vector orthogonal to the vector u=3, 1, -2. Then, u·v=0…

Q: For which value of k the two vectors u=(3,3,k) and v= (-4,8,1) are orthogonal? *

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Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (17, –18, –1) V

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Q: Determine R21, the vector from P2(5,2,–4) to P1 (3,–1,0). 2аx + Зау — 4а, —2ах — Зау + 4az 4ax + ay…

A: Consider the following vectors: P→1=3ax-ayP→2=5ax+2ay-4az…

Q: If the magnitude of the vector u is √2 and its direction is 225°, then its components are:   (1,…

A: Solution of question as follows

Q: Find the component of V, |V|= V5 in the direction of a vector from A(0,0, 4) to B(2,5, 0).

A: The vector joining the points A0,0,4 to B2,5,0 is given by, AB→=2-0i^+5-0j^+0-4k^=2i^+5j^-4k^ The…

Q: Find the vector z, given that u = ⟨1, 2, 3⟩, v = ⟨2, 2, −1⟩, and w = ⟨4, 0, −4⟩.      z = u − v + w

A: Given:                                                          u = <1, 2,…

Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·¤-A-D-A-A-D 3 +y-2 +2 1 1-2 +3…

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Q: Given the vectors, v = (1,–2,-3) and w = (3,– 2, 1), find the orthogonal projection of v onto w.

A: Since you have posted multiple questions, we answered the first question for you. If you want us to…

Q: What value(s) of a are necessary for vectors i = (2, a), and w = (4a, 3) to span R?

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = (5, 2,…

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Q: Find the vector z, given that u = (6, -3, 2), v = (0, 2, 1), and w = (-6, -6, 2). %3D Z = -u + 4v +…

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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: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) (10, -12, -2) %3D V =

A: Find the unit vector that is orthogonal to both u and v

Q: Find the vector z, given that u = (7, 6, 7), v = (2, 2, –1), and w = (4, 0, –4). z -u -v + 2w

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector