1. Initial point of vector v is ( 2, -1, 3) and the terminal point is ( -1, -3, 2) Write components of v. b. Write v as linear combination of the standard vectors i, j, k. c. Find ||v||. d. Find a unit vector in direction of v.

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: Given vector u = (3, 1) and v (1,3) , determine the value of 2u – 3v in component form.

A: Use component wise addition and multiplication for required answer.

Q: Let v = −→P Q, where P = (1, 1) and Q = (2, 2). What is the headof the vector v equivalent to v…

A: (1).    The components of vector v = PQ→ where Pa1,b1 and Qa2,b2are quantities…

Q: For what values of a and ß will the vector (a, 1, B) be orthogonal to (2, 0, 7) and (-1, 1, 2)? α =…

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Q: Which of the following pairs of vectors are linearly independent? Ou = (1,0) and w = (0,2). Ou =…

A: Linearly independent

Q: Let vi, ..., v be vectors, and suppose that a point mass of m,, ..., m, is located at the tip of…

A: Given: u1=-1, 0, 2   and     m1=2u2=2, 1, -3   and     m2=1u3=0, 4, 3       and     m3=4u4=5, 2, 0…

Q: Given the points A(1,2,3,) and B(2,-2,1) Find the Vectors A and B with respect to origin. Unit…

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Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Determine the length of each vector.

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Q: Given the vectors u=(2,1,1,1) and v=(3,2,-1,2) ,find the value(s) of such that  U•(u+tv)=16

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Q: Consider the points P(2, −1, 0), Q(5, 0, 0), and R(3, 1, √5). Find the coordinates of the vector QS…

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Q: Determine if the vector v is a linear combination of the remaining vectors.

A: Given vectors are: v=123; u1=110; u2=011 If the vector v is a linear combination of the remaining…

Q: given the vectors u = (2,4) y = (- 1,3) and w = (2, -3) Determine the values ​​of α and β such that…

A: Given vectors are  U = (2,4) so we can write it as=  2i + 4j ( i is the unit vector in x direction…

Q: Given vector u = (6, –1) and v = (2, –2) , determine the value of u – 2v in component form.

A: Given query is to find the indicated vector.

Q: Find the value of t such that the vectors v=(2t+1,-3,3t-2) and w=(7,4t+2,2) are orthogonal.

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Q: (iii) Suppose the vectors u, v, w are linearly independent. Show that the vectors u+ v, u-v, u-2v +w…

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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: Given the points A(-2, 3, 1), B(0, 0, 2), and C(-1, 5, -2) Express the vector v = (3,2,7) as a sum…

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Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. If vector AB = i + 4j…

A: Given  AB=i+4j-2k and B is the point (5,1,3)

Q: Use the given vectors to compute u + v, u − v, and 5u − 3v. u = (5, −2),    v = (7, 6)

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Q: Given vectors u = 1.3i + 4.8lj and v = -7.4i + 2j, u and v are: Parallel vectors. O None of these.…

A: Given vectors are u=1.31i+4.81j and v=-7.4i+2jTo check if the vectors are parallel they should…

Q: 7. Find the values of m that will make the following vectors perpendicular. à = (2m, 3,1), b = (m,…

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Q: 5) Find a unit vector that has opposite direction of the vector i - 2j + 4k.

A: First change direction of vector then find magnitude and write unit vector

Q: For each pair of vectors Calculate proju and the vector component of u orthogonal to V. a7…

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Q: Given the vectors u = (2,1,1,1) and v = (3,2, −1,2), find the value(s) of t such that I.  v . (u +…

A: Given vectors are u=2,1,1,1 and v=3,2,-1,2. To find value of t such that v.u+tv=16. Solution:…

Q: 4. Find the angle between each pair of vectors. Round to two decimal places as necessary. a) (V3,…

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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: 2. Given the points P(-1,3, 1), Q(0,5, 2), R(4,3, –1), (a) Find a nonzero vector orthogonal to the…

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Q: Given vector U= ⟨3,1⟩ and V=⟨-4,3⟩, find a linear combination of the vectors u and v of the form aU…

A: Solving simply equations and find the value of a and b by compairing both side of vector

Q: 1. Assume the lengths of the vectors 2a – b and å + 35 , assuming å = (2,1,3) and b = (-1,2,2) 2. If…

A: Using scalar multiplication of vectors and magnitude of vector concepts  we can solve this question

Q: Find the vector z, given that u = , v = , and w = . z = 8u − 2v − 1/2w

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Q: 3. The vectors i and y are each vectors of length 3 units, i.e., = | = 3. If + = V17, determine – j.…

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Q: 3. (a) Define the dot product of the vectors u = (a,, az) and v = (b,, b,), and state the formula…

A: a). The dot product of the vectors u=a1, a2  &  v=b1, b2 is the sum of the product of…

Q: a- Show that if v is any nonzero vector then is a unite vector . |||| b- If u = (3,4) , v= (3 ,-1)…

A: First assuming v in vector notation.

Q: what is u.v when u and v are two unit vectors with an angle of (pi/6) between them. if u=i and if v…

A: Given: u=i, angleθ between u and v=π6 let's assume v=xi+yjx2+y2 we know that angle between two given…

Q: 1. Given three vectors u =(1,–3,0), v=(2,1,–1) and w=(0,2,3). Determine: a. Bu + 4v – Sw]. b. Cosine…

A: 1. a.

Q: Let P(4, - 3) and Q(- 1,2) be the initial point and terminal point, respectively, of vector V. Find…

A: Solution  Find position vector

Q: 4.14. Determine whether vectors u and v are orthogonal, parallel, or neither for u =i and v = -2i+…

A: You need to verify by using orthogonal and parallel test of two vectors using their dot product.

Q: 2. Determine the value of c, so the given vectors are perpendicular: u=[-4c, 3], v = [-1, 2]

A: L

Q: Suppose u and v are nonzero vectors. What is the geometric relationship between u and v under each…

A: Given u and v are non zero vectors.

Q: Given vector u (-1, 5) and v = (5, 3) , determine the value of 2u – 2v in component form.

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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: 3. Consider two vectors v = and w =. (a) Decide if v and w are linearly independent.

A: (a) Given v = <0, 1, 2>  and  w = <1, 0, 1> Let av + bw = 0 => a(0, 1, 2) + b(1, 0,…

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 1 3, a +2b,…

A: The equation of the line PQ is : PQ=Q-P=12a+34b-(a+2b)=12a+34b-a-2b=-12a-54b The equation of the…

Q: Assume that the vectors a, b, c, and d are defined as follows: a = (8,3) b = (6,5) c = (4, -1) d…

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Q: Determine if the vectors t= %3D(-16, 24) and s= (3, 2). are orthogonal, parallel, or neither.

A: We have to calculate dot product and magnitude of the given vectors

Q: Find the vectors that satisfy the stated conditions. 23. (a) Oppositely directed to v (3,-4) and…

A: a) The given vector is v = <3, - 4>  To find vector opposite to given vector and half in…

Q: Given vector u (4, –1) and v = (-1, –5) , determine the value of v + 2u in component form.

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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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