Given vectors v=3i-5j, and w=-2i+3j, calculate the following: A) 3v-2w B) ||v-w||

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 14j as…

A: ANSWER IS GIVEN BELOW.

Q: or what values of aj are the vectors [ai,4,3] and a) orthogonal? b) Parallel? c) Have 45 degree…

A: If 2 vectors a⇀,b⇀  are orthogonal, their dot product a⇀.b⇀ =0 Let u=a1,4,3 and v= 3,-2,12 So,…

Q: What geometric relationship must two vectors have in order for ||u + v|| = ||u|| + ||v|| ?

A: The expression ∥u+v∥denotes the norm of u+v, ∥u∥denotes the norm of u and ∥v∥denotes the norm of v.…

Q: If the volume of the parallelepiped determined by the vectors A = i +ak, B = 8i-5j + ak and C = 2i…

A: Given vectors are A = i + αkB = 8i - 5j + αkC = 2i + 3j - 8k

Q: Find the area of the parallelogram that has the vectors u = ⟨3, −1, 5⟩ and v = ⟨2, −4, 1⟩ as…

A: Now

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i +j and i- 6j as…

A: Here we have to find the length of the diagonal.

Q: Find the area of the parallelogram determined by the vectors u and v.

A: Given any non-zero vectors.

Q: When two nonzero vectors w are called perpendicular or orthogonal?

A: Let two nonzero vectors are u and v Then the scalar product of the two vectors is given as,…

Q: Find the area of the parallelogram that has the vectors u and v as adjacent sides, where ||u|| = 2,…

A: The area of the parallelogram is ∥u∥×∥v∥×sinθ=2×12×sinπ3=24×32=123   Here θ= the angle between u and…

Q: What is the cross product of the vectorS 2i + 3j + k and 61 + 9j + 3k? Explain why your answer is…

A: Cross Product: Cross product of two vectors is the method of multiplication of two vectors. A cross…

Q: given two vectors v m which are perpendicular. under which condition is V+W perpendicular to V-W?

A: Since vectors v and w are perpendicular so, their dot product is 0

Q: The angle between two unit vectors e and f is π/6 . What is the length of e × f?

A: The angle between two unit vectors e and f is π6.

Q: For the three vectors a, b and C , it is found that à•bxT = 0. Which statement below is true? %3D

A:

Q: Given the vectors v 4i + 2j - 3k and w = 3i – 4j + k.. Find the angle between v and w.

A:

Q: Given three vectors, u, v, and w, if u (v x w) = 0, what geometrical result can be concluded?

A: We have to conclude the result of u→.(v→×w)=0→.

Q: Suppose vectors v, w, and z sum to the zero vector. If v = 8.2i - 3.8j and w = 4.1i + 1.3j, find z.

A: We have to solve

Q: What is the area of the parallelogram formed by the vectors v = (1,0, 1) and w = (0, 2, 2) tail to…

A:

Q: Show that if u+ v and u - v are orthogonal, then the two vectors must have the same length. What…

A: Hence the two vector u and v have same length.

Q: Given vectors ū = [3,2, –1] and v = [-2,2,4] , calculate the following: %3D %3D a) 2ū + 30 b) ū · v…

A: Use vector properties.

Q: Find the area of the parallelogram that has the following vectors as adjacent sides. u = & v =

A:

Q: If the volume of the parallelepiped determined by the vectors A = i + ak, B = 8i - 5j + ak and C =…

A:

Q: Find the value of a so that vectors U = ai + 9j and V 3i + 12j are perpendicular. %D a =

A: Since, We know that Two Vectors are perpendicular to each other if and only if their dot product is…

Q: In a triangle ABC, points E and F are on the sides AC and BC respectively, such that AE is 1/3 of AC…

A:

Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (6, 6, 0), Q = (3, - 5,…

A: Let the parallelogram be PQRS, whose 3 vertices are P(6,6,0), Q(3,-5,6) & R(3,1,4). Then, these…

Q: If vector AB = i + 4j - 2k and B is the point (5, 1, 3), find A.

A: Given,

Q: и %3D —3і + бј, w%3 -2i – 5j u = W =

A: Here I am attaching image so that you understand each and every step. Given option are not match…

Q: Given the vectors →u=−6i−3j and v→= 10i+5j perform the operations below. →u+→v=____________ →u−→v=…

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Q: 19. Show that the pair of vectors 8i+j and i-8j is perpendicular.

A:

Q: If the points with position vectors 10i+3j.12i-5j and ai+11j are collinear, Find the value of a.

A: The position vectors of the points which are collinear is: 10i+3j ,     12i-5j ,      ai+11j

Q: Given the vectors u = -i-5j and v =-3i+2j, find u v

A: Given vectors are  u=-i-5j     and   v=-3i+2j

Q: Given the vectors v = 4i + 2j +k and w = 3i – 4j + k. Find | 2v – w |

A:

Q: What is the angle of vectors A=5m South and B=15m 60° South of West?

A: `Vector is a quantity that has magnitude as well as direction. So we need to find the angle of…

Q: The area of the parallelogram whose adjacent sides are the vectors u and v is a) Ju · v| c) Ju x v|…

A:

Q: Given that the vectors ở = (1, 2– k,3) and b = (7, 4, k+2) are perpendicular, what is the value of…

A: Given vectors are: a→=1,2-k,3 and b→=7,4,k+2

Q: Given the vectors v = 2i+ 3j – k and w = 4i – 2j + 3k. Find the angle between v and w. %3D

A:

Q: Find the area of the parallelogram that has the vectors u = (3, -1, 2) and v = (5, -4, 1) as…

A: Area of the prallelogram using cross product

Q: Find the angle between the vectors u = (2, 5) amd v =

A: Given: There are two vectors: u=2,5v=4,-3 To determine: The angle between the given two vectors.…

Q: Show that if u+v and u – v are orthogonal, then the vectors u and v must have the same length. If 0…

A: As per our guidelines we are supposed to do only first question among multiple questions. To get the…

Q: Show that the points whose position vectors 2i+ 3j – 5k , 3i +j – 2k and 6ỉ – 5j + 7k are collinear?

A: Let the given vectors are  A=2i+3i-5k,B=3i+j-2k,C=6i-5j+7k. Find AB as follows: BA=2-3i+3-1i+-5--2k…

Q: Suppose that u and v are vectors in R? both of length 2/2 and that the length of u-v is also2 2.…

A: We will use expansion of u-v to find the angle

Q: ABC is a triangle. If D is the midpoint of AC, show that BA + BC = 2BD. Vectors

A: Consider the given information. Let's draw the triangle.

Q: Show that the indicated diagonal ofthe parallelogram determined by vectors u and v bisects the…

A: The given parallelogram is   Here, we are given |u|=|v| So, u+v is the required diagonal

Q: Which polygon is the result of reflecting polygon 1 through AB, then translating the reflected…

A:

Q: Suppose i and V are vectors such that ||ū|| = 2, |||| = 3, and the angle between u and ở is 60º. a)…

A: This question is related to vectors, we will use formula of dot product of vectors and basic…

Q: Given the vectors v = 4i + 2j + k and w = 3i – 4j + k. Find the angle between v and w .

A: We know, the angle between two vectors v→ and w→ is θ = cos-1v→·w→|v→| |w→|

Q: Find the value of a so that vectors U = ai + 12j and V = 31 + 9j are perpendicular. a =

A:

Q: Find the area of the parallelogram that has the vectors u = (2, -1, 5) and v = (3, -4, 1) as…

A:

Q: Given the vectors v =i+ 3j – 2k and w= 3i – 4j + k. Find the area of the parallelogram with sides…

A:

Q: Show that the points with position vectors 3i–5j, 4¿+j, 6¿+13j are collinear. If the point whose…

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.