If u, v are vectors such that |u || - 3, ||v|| - V5, and u v- 1, what is |u + v|| ?

Q: Find the length of the vector.v = (4, 3)

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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: Let u and v be two non-zero vectors in R". Which of the following options can we conclude are equal…

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Q: What can be said about the vectors u and v when the projection of u onto v equals u?

A: What can be said about the vectors u and v when the eprojection of u onto v equals u?

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

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Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (12, -16, -2)

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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 cross product of two vectors u=(2, -3, 1) and v=(0, − 1, 2) is 5. O True O False

A: Here is the solution:

Q: a) If possible, express w as a linear combination of vectors u and v. w = - (1,0, —7), и %3D…

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Q: let v = (1, 3, −2) and w = (2, −1, 4). Find all the vectors orthogonal to both v and w.

A: Given: The vectors v=1,3,-2 and w=2,-1,4. To find: The vectors orthogonal to both v and w.

Q: Which of the following vectors is perpendicular to v = (1, –1, 3) ? о (2, —1, —1) O (-1, –1, 2) о…

A: Two vectors (a, b, c) and (x, y, z) are said to be perpendicular when their dot product ax+by+cz=0

Q: a) If possible, express w as a linear combination of vectors u and v. w = (1,0, –7), u = (1,3,4), v…

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Q: Let v be a vector of length 2. If w = -5v, u = (-2, –2) and the angle between w and u is . then v x…

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Q: \(\) The vectors u= and V = are not orthogonal if and only if x=-136

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Q: Show that there are no vectors u and v such that 11u 11= 1, ||v|| = 2, and uxv= 3.

A: If u and v are two vectors, and the angle between these two vectors is θ Then the magnitude of the…

Q: A vector u is a positive multiple of . Vector v = with a , what will be the signs of d, e, and f?…

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Q: Prove that if the vectors a,b parallel, then āxb=0. are %3|

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Q: Suppose that u and v are vectors in 3-space such that u ||= 5 and u · v= 7. Find: (a) u · u = (b) v…

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Q: Verify the Pythagorean Theorem for the vectors u and v.u = (4, 1, −5), v = (2, −3, 1)

A: Given   The vector u = (4, 1, −5), v = (2, −3, 1) Pythagorean Theorem for the vectors

Q: Show that if u and v are n-vectors, then u · v = uT v.

A: Consider the n vectors  u=u1u2u3.un,v=v1v2v3.vn

Q: Find the values of x such that the angle between the vectors u = (2, 1, -1) and v = (1, x, 0) is…

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Q: Prove that for any vectors u, v, w , the set span{u+v,u – v, 3u – 3v + 2w} contains u, v, and w .…

A: A vector v is said to be contained in span of set S  (span(S)) if vector v can be written as a…

Q: The vectors u and v are ________ if and only if u ∙ v = 0.

A: If the dot product of two vectors is zero ,                    If and only if they are orthogonal;…

Q: Show that the vectors u=, v= , and w= satisfy the following properties of the cross product. и хи30…

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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: Give an example of vectors in R^3 that spans R^3. (show works)

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

A: In this question we will use basic of calculus i.e vector calculus. We will simply find the cross…

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: Suppose u, v, and w are vectors in R³ and W = span{u,v,w}. Let x be a vector in R³ that is…

A: We are given that x is orthogonal to each of the vectors u, v, and w. Thus, x is orthogonal to any…

Q: Suppose ~u and ~w are vectors in R^n . Prove that if ~u and ~w are parallel vectors in the same…

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Q: Prove that two vectors v = (a, b) and w = (c, d) are perpendicular if and only if ac + bd = 0

A: we have to prove that the two vectors v=a,b and w=c,d are perpendicular if and only if ac+bd=0

Q: Find the angle between the vectors u and v if u = (2,3,5) and v = = (1,–4,3) in

A: First we convert this into vector then find the angle

Q: Show that if u and v are vectors in the three-space, then ||u x v||? = ||u|| ||||² – (u · v)²

A: u and v are vectors.

Q: Verify the triangle inequality for the vectors u and v.u = (4, 0), v = (1, 1)

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Q: Let u = (2, 0), v = (-2, -4), and w = (-4, 1). Find the vector æ that satisfies 4u – v+ x = 9x + w.…

A: Solution:-

Q: Under what condition for the real numbers a,b the vectors (b,-1)(2,a) are linearly related

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Q: What does (a b c)=0 imply with respect to the vectors: a,b,c

A: Consider the given information. The given vectors are a, b and c. Geometrically, the scalar triple…

Q: given the vectors from R3 v, = (2 0 3), v2= ( -1 3 0), v3=(2 4 –1) %3D (-5 0 3) belongs to span{v,,…

A: Given vectors are v1→=2,0,3, v2→=-1,3,0, v3→=2,4,-1. To determine: u→=-5,0,3 belongs to span v1→,…

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: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: Consider two vectors ~a and ~b such that ~a x^b = ~0. What can be said about vectors ~a and b?…

A: We have to give the reasons

Q: 8. If the vectors in the figure satisfy |u| = |v|= 1 and u + v + w = 0, what is w ? u W V

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Q: Verify the triangle inequality for the vectors u and v.u = (1, −1, 0), v = (0, 1, 2)

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Q: For the vectors u (1,0, 1) and v (0, 2, 1), u x v = %3D O A. (1, 2, 0) O B. (1, 2, -2) OC. (2, 1, 2)…

A: Given. The vectors u = 1, 0, 1 v = 0, 2, 1 We have to find u×v

Q: 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

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Q: (True/False) For any three-dimensional vectors u and 7, we have u x vx u.

A: The given statement is true.

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 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 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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