27-30 - Writing Vectors in Terms of i and j Write the given vec- tor in terms of i and j. 27. u = (1, 4) 28. u = (-2, 10) 29. u = (3, 0) 30. u = (0, -5)

Q: Find the initial point of the vector that is equivalent to u = (2, 2, 4) and whose terminal point is…

A:

Q: w = (-2,0) , v1 = (-1,2), v2 = (4, –8) , vz = (-1,1). If possible, express w as a linear combination…

A: Let us assume -20=a-12+b4-8+c-11. So,               -20=a-12+b4-8+c-11⇒-20=-a+4b-c2a-8b+c⇒a=4b-2,…

Q: 1. Using the vectors u = [4, -3] 3 = [7, 1] and w = [-5, 3], evaluate the following, if possible. If…

A:

Q: = 2. Are the vectors V = (2, — 4, 1) and w Show work and briefly explain. (3, 2, 2) orthogonal? 3.…

A:

Q: How do you find the stable vector? P=  1/4 3/4         4/7 3/7   ---I understand how to create…

A: Given Matrix , P=14344737 We need to find a stable vector X ,which satisfies PX=X and X =AB…

Q: Are vectors v = ⟨ − 2 , − 3 ⟩ and u = ⟨ 6 , − 4 ⟩ orthogonal? Yes or No:

A:

Q: 12. For which values of parameter a, the vectors. °u = (1, a, 2) and °v = (a, 4, 4) are

A:

Q: 9. Given vectors u = [- 2,6.7] and v = [3.1.–4]. determine .

A: From the given problem:   u→=-2,6,7⇒-2i+6j+7kv→=3,1,-4⇒3i+1j-4k   So,   u→×v→=ijk-26731-4

Q: 11. Given vector u = (2, a, 3), vector v = (1, -3, b) and u x v = (13, -5, -7). Find a and b.

A:

Q: Of the vectors u = (2, -1); v = (-1, -2); w = (-4, 2) and o = (4, 2) are orthogonal:   w and o u…

A:

Q: 1. Determine whether the vectors vi (1,2,3), v2 (2,4, 5), and v3 (1,0,0) are independent.

A:

Q: how can one show that three vectors span R^3?

A:

Q: 10. Vector q is a middle point for vector u and v; and middle point for vector b and d. Given that…

A:

Q: 1. Consider the vectors (2, 1,0, 2], [3, 1, 0, 1], [1, 1,0, -1] in R'. Decide whether they…

A:

Q: 9. V =|-1 Write the vector as the linear combination of the basis vectors 3 4 and u, =|- 3 u, = 2…

A:

Q: 5. If we have two vectors (V₁ and V₂), V₁ is a vector perpendic through the points A(1, 2, 5),…

A: Introduction: When a vector is along the direction in another vector, the two vectors are parallel…

Q: where u = (1, 1, 1) and v = (1,2, 3)? For what values of a and b the vector w = (6, 8, 10) is a…

A:

Q: (2,1, –4,0), v = (-1,-1,2,2), and 19. Find two vectors of norm 1 that are orthogonal to the vectors…

A: We have to find the basis of these vectors, which are independent. A=2-131-12-425024~I4 and they all…

Q: 1-4 - Operations with Vectors Find u|, u + v, u - v, 2 u, and 3u - 2 v. 1. u = (-2, 3), v= (8, 1) 3.…

A: 1). Given vectors are u=-2,3, v=8, 1. To find: u, u+v, u-v, 2u and 3u-2v. Solution: We have u=-2,3…

Q: Let u = (1,2,-3,0) and v = (5,0,4,1) are vectors in R. Then the distance between u and v is:

A: Given The given values of u and v are and . Apply the Euclidean distance formula.

Q: 11. Given đ = (2, x, –3) and b = (5,–10,y), for what values of x and y are the vectors collinear?

A: We have to find the values of x and y for which bothe the vectors are colinear

Q: 2 aj = a2 = az = b = Determine if vector b is a linear combination of vectors a1, a2, and аз. Show…

A:

Q: --8-9--8-- 7 1. Are the vectors u =| and w= 10 independent? 4 12 2 and 3 3 independent? 5 2. Are the…

A:

Q: 9. Let ū = (4, -6), T = (-2,4), and = (6,4). (a) Are ī and ū orthogonal vectors? How about ĩ and w?…

A:

Q: 11. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors…

A:

Q: let the vectors u = (- 2, -9, -8) and v = (- 4, -4, T) the value of T so that u and v are…

A:

Q: 6. Find the angel between two vectors ī= (-1, –1,2) and w= (2,3, –2). %3D

A:

Q: Find two different combinations of the three vectors u = (1, 3) and v = (2, 7) and w = (1, 5) that…

A:

Q: 9. (a) are perpendicular to each other. Determine the algebraic condition such that the vectors č=…

A:

Q: 5. (a) Are the vectors (1,3, 2), (2, 1,3) and (3, 2, 1) linearly independent? (b) Are the vectors…

A: Explained below

Q: write the given vector in terms of I and J. u={-8, 10} u=???

A:

Q: 1. For what value(s) of r (if any) is the vector (-2, 14, r) a linear combination of the vectors (2,…

A: We need to find r.

Q: If the vector v has initial point P, what is its terminal point? v = (-7, 0, 7), P(8, 0, –8) (x, y,…

A: in 3d space, if point P(X1, Y1, Z1) is the initial point and point T(X2, Y2, Z2) is the terminal…

Q: 1. If vectors u =(3, 3), v=( 13. -7), and 2w +3u-v=(4,-4) what is the coordinate of vector w? 2.…

A: For any vector x which is given as a,b, then a and b are the coordinates of the vector x. The…

Q: 3. (a) Find the terminal point of the vector that is equivalent to u = (2, 3) and whose initial…

A:

Q: 5. Let u be the vector with initial point (2,0) and terminal point (3,2). Let v be the vector with…

A:

Q: -2 is a linear combination of the vectors 4. For which value of k the vector u = 3 2 3 and v2 of the…

A: Given the given vectors are u=1-2kv1=30-2v2=2-1-5

Q: 7 For what value of k are the vectors u Select one alternative: Ok=-1 Ok=-2 Ok=1 Ok=2 (1,-1,-1) and…

A:

Q: Find all vectors v = (a, b, c) that solve the given vector equation. vxi = 2) Ov= (a, 2, 0) with a…

A:

Q: Mount Holyoke College, Massachusetts, USA - Can the vector (3, 1, 1) be expressed as a linear…

A:

Q: 7. and V -8 are orthogonal. 15 The vectors u = %3D L-7 True

A:

Q: If vectors u =(3, 3), v=( 13. -7), and 2w +3u-v=(4,-4) what is the coordinate of vector w?

A: The given vectors are: And, Let the coordinates of vector w be, Substitute the coordinates in…

Q: Find the angle between the vectors (approximate to the nearest degree): u = [0, 1, 1] and v = [1, 2,…

A:

Q: Express the vector (0, -1) linear combination of the vectors (1, 1) and (-1, 1) as a The correct…

A:

Q: 1. Are the vectors (-3, 0, 4), (5, -1, 2) and (1, 1, 3) linearly dependent in R3? a. Yes b. No

A:

Q: Find two unit vectors orthogonal to both (2, 3, 1) and (-1, 1, 0). LO î + 27 (F (smaller i-value) î…

A: Use the given information.

Q: a linear combination of the vectors Can we express the vector a = (2, – 5, 3) as e = (1, 1, 1), ez =…

A:

Q: Express the indicated vector w as a linear combination of the given vectors u,v if possible. w =…

A: Given that, W = ( 1, 0 , -7) u = ( 5, 3 , 4) V = ( 3, 2, 5) Let the a  and b be the any scalar…

Q: 8. a. Using the vectors = (3, 3, 1) and ỷ = (-1, 2, –3), verify that the following formula is true:…

A: