For each statement, determine whether it true or false, and justify your answer. a) In R³ if two lines are not parallel, they must intersect at a point. b) For u, v, w in R", if u +w=+w then u = v. c) There are no vectors u and 7 in R" such that ||ū|| = 1, ||v|| = 3, and ū - v = 6.

Q: If ū and i are two vectors, prove the identity ld + 레? + |d - 비? = 2| + 2|미2

A: This question is based on vector multiplication.

Q: ude 5. Find the area of the triangle created by the

A: Given a, b and c are three vectors with the same magnitude 5.

Q: u = (5,-1, 2) and v = (2,-1,-3) Compute the following: a.) v b.) lul c.) uv d.) projuv e.) The angle…

A:

Q: Let ū= (2,3,-5) and = (-4,-6,5). Determine a vector equivalent to 2 - 3 v Express - using unit…

A:

Q: Suppose that u,v are two vectors such that Ju| = 3 and |v| = 4. Let 0 represent the angle between u…

A:

Q: Vectors in R must have two or more values. A) True B) False

A: Ans: B) False

Q: 4. a) Givenā = [-5, 2, -3],6 = [7,-4, 1], c = [x, -2, z], and a × c =b, find x and z. b) Find a…

A: Given,  a→=-5,2,-3,  b→=7,-4,1 , c→=x,-2,z

Q: Prob. 2. ū and i are two vectors. If |피 = 4, [히 =3 and 2(ü, ü) = 2π/3. Find: a) ü.ㅎ b) ū.u c) |3ü +…

A:

Q: Lets vectors V and U be such that |v|=3 and |u|= 4. the angle between v and u is 30 degrees. find…

A: Given: u→=4    and   v→=3 Angle between vectors u and v is: 30°

Q: State the condition(s) that: a) two vectors can be equal vectors. b) two vectors can be opposite…

A: To state the conditions for a given vectors.

Q: For the following, let u = (3, –6) and v = (2, 1) %3D a. Find u + 3v b. Find the angle between the…

A: Hey, since there are multiple sub-parts posted, we will answer first three sub-parts. If you want…