Letu= (1,0,1,0,1) (A) Find a nonzero vector that is orthogonal to u(hint: your vector does not needto be complicated!). (B) Find‖u‖ (C) Find a unit vector in the direction ofu .(d) Find the vector component of u along a= (1,−1,2,−1,0)(that is,find projau) and the vector component of u orthogonal to a

Q: Qe A) Find the vector 5 unit length in the direction of vector perpendicular to the iHane which…

A: We have to find the perpendicular vector first.

Q: 6. Let a = (1, 0,3) and u = (2,-1,5). a.) (5 pts.) Evaluate projau. b.) (5 pts.) Find a vector that…

A:

Q: 23. Are the vectors u = and v = orthogonal? Explain.

A: Two vectors are orthogonal, if their dot product is equal to zero.  The formula to calculate dot…

Q: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

Q: For the vectors A=x + 2ŷ – î = (1, 2, – 1), B=ŷ + î = (0, 1, 1), C=î-ŷ = (0, 1, 1), a) Prove that Ax…

A: Correct last vector coordinates representation

Q: b) Consider the vectors u = (2c, 2, −4), v=(c, c, 3)and w = (-1, 2, 3). Find the value(s) of…

A:

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…

A:

Q: Let u = (4, 1, 5), v = (2, 1, 3) and w = (-a, 2, a). (a) Find a vector of length 6 in the opposite…

A:

Q: Find axb, a vector orthogonal to both vectors a' and b. a = (-3, 2, 1) and =(4, -2,5)

A:

Q: Q2/ (a) Let A (2,3,0) and B (-1,- 2,- 4) be two points. Find the vector AB in terms of the standard…

A: The detailed solution is as follows below:

Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A:

Q: Find a unit vector in the direction of u =

A: Here is the solution:

Q: use the vectors u = , v = , and w = a) Find which pair(s) of vectors from that set is/are…

A: We have to check

Q: find the angle between vector A = and vector B = then write A as a sum of a vector parallel to B…

A:

Q: A= (-5,12) B=(4,6) Assuming A and B as vectors, calculate the projection of vector B onto vector A.

A:

Q: what is the distance between the vectors  u = (0,1,2,3) and  v = (1,0,4-1)

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: Let u =[3, -1] and v = [0, 1] can you find the vector[h, k] that is not in Span{u,v}? either give an…

A:

Q: (b) If u and v are vectors in R' such that ||ū|| = 1 and |||| = 2 then u · i# 10.

A: The angle between two vectors and Dot product in R3 is related by