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Q: If v is a vector,then v + (-v)=.................

A: If v is a vector, then v+-v=___.

Q: 81. Given r = (-3, 4) and s = a. Find the product ||r|||s||. (9. – 12). b. Find r· s. c. Based on…

A: Given:r=-3,4 and s=9,-12Formula:u=u.u

Q: Find a vector b such that |b| = 1/2 that is parallel to a = but with opposite direction.

A: Given that: |b|=12a=<-6, 3, -2>

Q: Suppose A and B are non-zero vectors in R. If A•B = 0, then A and B are parallel. True False

A: Follow next step

Q: a. (a+ (а x b)) Choose... (a x b) + (b x a) Choose... аx (а.b) Choose... а. (а х b) Choose...

A: It is vector calculation

Q: Given vectors u and v in the diagram below, shade in all linear combinations cu + dv for (a) -1 1…

A: (a) Shade the linear combination.

Q: For the vector a,b,c ∈ IR3 a+b+c=0 and ===1 then ?

A: We will first assume a=(a_1,a_2,a_3),b=(b_1,b_2,b_3) and c=(c_1,c_2,c_3).Now will will use…

Q: (Boas, 3.4.17) Find three vectors (none of them parallel to a coordinate axis) which have lengths…

A: Let the three coordinates be A3,8, B3,4 and C7,4. Let us check that whether they form a right angled…

Q: If a,b,c are vectors such that a.b=a.c,a×a=a×c, then show that b=c

A: Given, a,b,c are vectors such that a·b=a·c, a×a=a×c To prove: b=c

Q: 2. Explain what it means for vectors to be each of the following: a) equal b) opposite c) collinear

A: A) equal vector

Q: a, b, c are non-zero vectors and a is perpendicular to both b and c. If |a|= 2, \b|= 3, |c|= 4 and…

A:

Q: 39. The vertices A, B, C of a triangle have position vectors a, b, c respectively. The area of this…

A:

Q: If a and b are vectors then ||a × b||²+ (a .b)² OA. |la |||| OB. ||axb|| OC. Ja.b| OD. II

A: Given:-  a and b are vectors To find:- ||axb||2 +(a.b)2 = ?

Q: State the hypothesis and the conclusion of the given statement

A: Given: All squares are rectangles.

Q: Let A = (1, 1, -1), B = (-3, 2, -2), and C = (2, 2, -4). Prove that ABC is a right-angled triangle.…

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: 1. The vertices of a triangle are located at A(4,1, –3), B(-2,5,4) and C(0, 1, 6). Using vector…

A:

Q: For what values of c are the vectors and perpendicular?

A: we will use dot product of two vector.

Q: Prove that An (BUC) = (An B) U (An C).

A:

Q: Which vectors, drawn on a grid from one point (on the "cross-hairs") to another have integer values?

A: Y-component of A →…

Q: We define a median vector of a triangle to be the vector from a vertex of the triangle to the…

A: Let ,The triangle be ∆ABC A(x1, y1, z1)B(x2, y2, z2)C(x3, y3, z3)AM→ , BM→ , CM→ be the medians

Q: If vectors a, b and c are coplanar, show that ↑ ↑- ↑ 11 C -->> a. a a.b a c= 0. ↑ ↑-

A: Introduction: Coplanar vectors are those in a three-dimensional space that are on the same coplane.…

Q: Two vectors u, v in Rº have lengths 4 and 4, respectively. It is also true that u- v = 0. What is…

A:

Q: Is the following statement correct? If A, B, C, and D are distinct nonzero vectors represented by…

A: A, B, C, and D are distinct nonzero vectors represented by arrows from the origin to the points A,…

Q: 1. Find the area of the parallelogram spanned by the vectors a = (1,0,1), b=(-2,1,2) A. √5 B. 3 C.…

A:

Q: If a and b are vectors with the same initial point and angle between them, prove that||a - b||2 =…

A: Consider the given expression as, a-b2

Q: A Problem. If A and B are vectors in R" and B + 0, let P = ProjR A and show that ||| ||A-P|| |||° =…

A: P is Projection of vector A on to B

Q: Given that a, b, c, and d are vectors in R³. Is it possible to calculate (à x ¯`). (c · (c + d ) ? ?…

A:

Q: For the vector a,b,c ∈ IR3 a+b+c=0 and ===1 then ?

A: Since we have given a,b and c are in R^3 so let a=(a_1,a_2,a_3) b=(b_1,b_2,b_3) and  c=(c_1,c_2,c_3)…

Q: Let A and B be nonzero vectors and let C = ||B||A+ ||A||B . Show that the measure of the angle…

A:

Q: Let V = (a, b, c, d), such that a = 2b − c, b = 2d − 3c, and d = a − b + c. Find the dimension of V…

A:

Q: This exercise illustrates how vector arithmetic can be used to prove propositions in plane geometry.…

A: (a) Here, u=v=u+v=1. ⇒u2=v2=u+v2=u+v·u+v ⇒(u+v)·u+v=1⇒u·u+2u·v+v·v=1⇒u2+2uvcos(θ)+v2=1⇒1+2…

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.