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

Q: What geometric relationship must two vectors have in order for ||u + v|| = ||u|| + ||v|| ?

A: The expression ∥u+v∥denotes the norm of u+v, ∥u∥denotes the norm of u and ∥v∥denotes the norm of v.…

Q: Find the area of the parallelogram that has the vectors u = ⟨3, −1, 5⟩ and v = ⟨2, −4, 1⟩ as…

A: Now

Q: Find the unit vector in the direction of v and verify that it has length 1.

A: If vector u is given, then the unit vector in direction of vector u is given as,

Q: C A

A: We use Triangle law

Q: Find the smallest angle between the vectors v = (1,1,2) and w= (2,4,5).

A: The given vectors are,

Q: Find a vector, AB , with magnitude 4 in the direction of PQ where P and Q have coordinate (5,0, 8)…

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Q: Find the area of the parallelogram determined by the vectors: u = (1,0,–3),v = (2,3,0)

A: By using formula  Area of parallelogram

Q: Find the angle 0 between the vectors. u = (2, 2), v = (4, -4)

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Q: Determine the two unit vectors that are orthogonal to i = (1,2). Which two unit vectors are parallel…

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Q: Find two vectors v1 and v2 whose sum is ⟨−5,0⟩, where v1 is parallel to ⟨5,1⟩ while v2 is…

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Q: What is the resultant of vectors a and b? ( A ) GL B

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Q: For what values of c are the vectors [-8, c, 4] and [c, c²,c] orthogonal?

A: For orthogonal,dot product of vectors is equal to zero.

Q: Find the vector v of length 6 that has the same direction as the unit vector (1/2, V3/2).

A: Consider the following values: magnitude=6unit vector=12i^+32j^

Q: Find the angle θ between the two vectors.u = (3, 3), v = (−2, 2)

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Q: is The unit vector in the direction of v=(4,0,–3)

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Q: What is the angle measure between the vectors u = (-5, 8) and v = (3, 9)?

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Q: Find the angle between the pair of vectors below. u = (2,3) and v = (-2,5)

A: Given query is to find the angle bothe vectors.

Q: Two linearly independent vectors in R3 span R2, is that true

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Q: Find the angle θ between the vectors.u = (1, 1, 1), v = (2, 1, −1)

A: The vectors are To find the angle between the given vectors, use formula

Q: Find the vector v with the given length and the same direction as u.||v|| = 3, u = (0, 2, 1, −1)

A:

Q: What is the magnitude of the vector (2, 4, –4)?

A: FORMULA

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (3, 2, −1), v = (1, 2,…

A: Now,

Q: Find the angle θ between the vectors.u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

A: The given vectors are, u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

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: Determine a unit vector in the direction in whichf(x,y) = 4x³ y² increases most rapidly at point…

A: Given that : - f(x,y)=4x3y2    at  P(-1,1) A function f(x,y) increases most rapidly at pointy P(a,b)…

Q: 4. Show how to find a vector ẽ = c – Ab that's perpendicular to b and is a linear combination of b…

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Q: Find the angle between the two given vectors. u = (1, –4, 1), v = (0, 2, –2)

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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: nd the angle (to the nearest tenth of a degree) between the vectors  u = and v=

A: Angle between vectors u and v is θ = arc cosu.vuv

Q: Find the vector with length V17 and same direction as i= (7,0, –6).

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Q: The volume of the parallel pipe formed by three vectors A, B, and C is 50 cubic units. if A(-2,6,3),…

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Q: Find nonzero vectors u, v, w that are perpendicular to (1, 1, 1, 1) and to each other.

A: Then   -------------(1) Also  --------------------(2)

Q: Find the angle θ between the two vectors.u = (10, −5, 15), v = (−2, 1, −3)

A: The given vectors are To find the angle between the given vectors, use the formula

Q: Find the angle between the vectors u (2, –1) and v = (1, 1).

A:

Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (– 6, – 1, 3), Q = (- 1,…

A: The corresponding position vectors with respect to origin are,…

Q: Find the vector v with the given length and the same direction as u.||v|| = 5, u = (√5, 5, 0)

A: Let the vector u is:   Now, The modulus of vector u is :                                     The…

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (2, −1, 0), v = (−1,…

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Q: how is C equal to the difference of vectors A and B?

A: Dear user, Please read the question. We need to express Vector A in terms of sum of  B and C.

Q: Find the area of the parallelogram that has the vectors u = (5,-1, 4) and v = (2,-3, 1) as adjacent…

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Q: Find the angle θ between the vectors.u = (3, 1), v = (−2, 4)

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Q: Find the angle θ between the vectors.u = (0, 1, 0, 1), v = (3, 3, 3, 3)

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Q: Find a unit vector perpendicular to plane PQR. Р(1, -1, 2), Q(2, 0, — 1), R(0, 2, 1)

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

Q: Use the vectors u = (2, 2), v = (-5, 1), and w = (2, -2) to find the indicated quantity. (v . u) –…

A: Given that u=2,2,  v=-5,1  and  w=2,-2.. Compute v·u as follows. v·u=-5,1·2,2=-52+12=-10+2=-8

Q: What is the resultant of vectors a and b? (

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Q: State the condition that the two vectors i and y are perpendicular. Find the value(s) of k such that…

A: If two vectors are perpendicular to each other, then their dot product is equal to zero.

Q: Find the angle θ between the vectors.u = (−4, 1), v = (5, 0)

A: u = (−4, 1), v = (5, 0)

Q: Let u and v be vectors. If their dot product is zero what is the angle between u and v (in degrees)?

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Q: Find unit vectors Parallel to the YZ Plaane and PerPendicular to the Vector V = 51-j+2k ?

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Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (1, 0, 1, –4)

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