1 6. Consider the vectors i 2, and w 3 4 Compute the dot product w = W

Q: bäi The cross product of the vectors 3ax + 4ay – 5az and -ax + ay - 2az * ,is -3ax+11ay-7az O -3ax +…

A:

Q: 10. Let v = [1, 1] and w = [2, 1] be two vectors: find the project of v into w d bu [1 11. 11. 1, 2,…

A:

Q: 18) a) Find a unit vector that is orthogonal to both u = and v = . b) find the area of the…

A:

Q: 4. Suppose the vectors u and w are in space R, then u - 2w and u+ 2w are perpendicular if (a) ju =…

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the…

Q: 3. [7.3] Determine the dot product between the two vectors below if there are 135° between them as…

A:

Q: 1. Given the vectors U = i- 2j+k, V = 2i+j+k and W = 3i – j+ 2k, compute the following: U (c) ||U||

A: The solution is :

Q: 15. Given three independent vectors w, "'z innd wz, let 2 2=[Wi #2 #3 2 1 0 1 c Then, the vectors v,…

A:

Q: Г10] Let ÿ = 7 and i = -2. Write y as the sum of two orthogonal vectors, j1 parallel to u and j,…

A:

Q: 1. Consider the following vectors in R³: 2 3 y= |1 3 -1 2 -4 Which of the following equals ||||7|T –…

A: According to Bartleby guidelines we can solve only the first question, in next step see the…

Q: Find the magnitude R and direction 0 of the resultant vectors. 7.0N 5.0N 5.0N 6.0N 2.5N 80 20 30 10…

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…

Q: 6. Consider the vectors u = (1,–2), v = (4,3), and w = (9,4). Find scalars k and k2 such that w =…

A:

Q: +5 c) Let y = n44| and u = is Span{u} and one orthogonal to u. where n=9. "t. Write y as sum of two…

A: y=nn+4 and u=n+5n-1. We have to write y as the sum of two orthogonal vectors, one is span{u} and one…

Q: 27. Given the vectors a and b, where a = 21 – 2j + 2k and b = 3i – j + 2k are coplanar vectors, a x…

A: Given vectors are a=2i-2j+2k and b=3i-j+2k are coplanar vectors. To find: a×b Solution: We have…

Q: Consider the following vectors: 2 3 u = 3 v = -4 W = 17 2 Express w as a linear combination au+bv.…

A: The given vectors are  u=23-1  , v = 3-42,  w= 017-7

Q: 2. Consider the vectors in En : e, = (1; 0; 0); ez = (0; 1; 0); ez = (1; 0; 0); Write down the…

A: Solution :-  the given vecots are e1 = ( 1; 0; 0 )  , e2 =  ( 0; 1; 0 )  , e3 = ( 0; 0; 1 )  and  (…

Q: Consider two vectors →A=Ax^i+Ay^j+Az^k and →B=Bx^i+By^j+Bz^k. Scalar product of these two vectors…

A: The scalar product can be evaluated using the two formulas given in the question. We will take the…

Q: Which of the following vectors is parallel to the vector v -2i +j+ 2k O 2i -j-2k O 4i + 2j + 4k O 2i…

A:

Q: 10. Given two vectors u = [2,4] and v = [6,2]. determine the projection of u on v.

A:

Q: -2 [5a] Find the value of a such that the vectors u =a +4 and v = |2 are orthogonal.

A: Please refer the attached image for complete solution. Given: u = -2a+4   1  & v = 5a 2 0 are…

Q: 4. Given the two vectors rA =-ax - 3ay - 4az and re= 2ax + 2ay + 2 az and point C (1, 2, 3) find: a)…

A:

Q: 4. Consider the vectors u,v and w are defined, u = 3i-j+4k, v = 4i – 2j +6k and w= 5i+2k (a) Express…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 4.18. Given vectors u = 3j – - 6k and v = 6i – 4j – 2k, find the dot product of u and v.

A:

Q: 7. Consider the following two vectors: u = (5, –3) and v = (2,3) (a) Evaluate |u| and |v|. (b) Find…

A: As per guidelines, we are supposed to do only the first three parts of multipart question. If you…

Q: linear algebra question:

A: The orthogonal projection is given by,

Q: 17 (c) Find a unit vector which is orthogonal to the vectors -1 2 and 1 -3 5

A: First we will find a vector which is orthogonal to both given vectors and then we will find the unit…

Q: 1.17. Given A=(10/V2)(ª, + a.) and B=3(a, +a,), express the projection of B on A as a vector in the…

A:

Q: If the triple scalar product of the vectors A = i+ 3j + k, B = 2i -j-k and C= ai + 7j + 3k is zero ,…

A:

Q: . Show that the vectors a = 3i-j+4k, b = i-3j-2k and e = 4i-3j+2k are linearly independent. Find…

A: Note:- We are entitled to solve only the first question, unless specified. Given vectors: a=3i-j+4k,…

Q: 14. Consider the following vectors: 1 4 8 -3 u = v = -5 1 a. Find the scalar product (dot product)…

A:

Q: 22. Given that the vectors a = 3i-4j-4k, b = 2i-j + 3k, and c = 4i-3j +5k. The %3D %3D projection…

A: Here let d= a+b d= a + b⇒d = 5 i -5j -kProjection length of vector d = (a+b) on c is given by |d|…

Q: 11. What is the vector which is orthogonal both to 9i + 9j and 9i + 9k? B. 81i – 81j – 81k A. 81i +…

A:

Q: Given the 3-dimensional vectors: A = (xy)i + (2yz)j +(3xz)k B = (yz)i + (2xz)j +(3xy)k Determine the…

A: Here given vectors as A=xyi+2yzj+3xzkB=yzi+2xzj+3xyk

Q: 5 Given that p andr , find in column vector form: 4 p-r ep-2

A:

Q: 1. For the following vector à and B, find à + B and B – Ả. Calculate |Ả + B| and |B - Ả . Å = 3ï+ 27…

A:

Q: 4.4.2 The vectors defining a particular system of oblique coordinates are c = (j + k)//2. a = i, (a)…

A: Given - a = i , b = j and c = (j+k)√2 (A) We have to find P , Q and metric P¯P P =…

Q: 3 as a linear combination of the vectors: 0 Lo] 1. Write the vector v = 6

A:

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: 5. Show that the vectors a = 3i-j+ 4k, b =i-3j–2k and e = 4i– 3j+2k are linearly independent. Find…

A:

Q: Compute the distance between the following vectors: 2 2 w = 3 v = -4 1

A: Hope it is useful

Q: 10. Let the vector v = 2i -3j + k, and the vector w = = -i+3j+ 2k. Find v x w.

A:

Q: 5. Let A =-ai+3j–2k and B = 4i + ßj+8k (a) Find a and ß if A and B are parallel. (b) Determine the…

A:

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: Which of the following vectors is parallel to the vector v -2i +j-2k O 4i-2j+ 4k O 2i-j-2k O 2i…

A: the vector will be parallel if they are multiples of one another that is u=cv

Q: 98 25) Gvon vectors v= 30tj and w=-2i -j. Decompose v into two vectors V, and Vz, where V, is…

A:

Q: and v2 = -3 3. be two -8- Question ( Let vi %3D vectors in R. Show that v belongs to span {v1, v2 }.

A:

Q: (b) Find the values of s such that vectors -si – 2j+ 5sk and 9si + j+3sk are orthogonal.

A: The given vector are -si-2j+5sk and 9si+j+3sk

Q: Which of the following vectors is parallel to the vector v = 2i -j– 2k O 4i – 2j + 4k O 2i + j+ 2k…

A:

Q: 4.15. Given vectors u = and v =, find the projection of u onto v.

A: Proceed as shown below...

Q: et x = [7, -4, -8] and y = [-6, -6, –10] be vectors in R'. Compute the following: %3D a+y [ -8x = […

A: Let's find.

Q: s such that vectors –si – 2j+5sk and 9si +j+3sk are orthogonal.

A:

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.