let A = si-j+ k which pairs of vectors ave @ perpendicular. ? O parallel. ? B=i-SK, f C=-15i+3j-3K. %3D

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: 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: The vectors A 5i + 7j – 8k and B 3i + yj + zk are known to be parallel. Find y and 2 y = = Z

A:

Q: If u = 5i - j+ k, v =j - 5k, w = -15i + 3j - 3k. Which vectors, if any, are (a) perpendicular? (b)…

A:

Q: Consider the following points P and Q. a. Find PQ and state your answer in two forms: (a, b, c) and…

A: (a) The vector joining two points P and Q is defined as, Where, the vectors P and Q are the…

Q: Let u =j- 3k, v = - 9i + 3j – 3k, w = 3i -j+ k. Which vectors, if any are (a) perpendicular? (b)…

A:

Q: 33. If 0 is the angle between two nonzero vectors v and w, and v· w < 0, what is the range of 0?…

A: Use the geometric definition of the dot product to calculate the angle between two non        zero…

Q: 39. For each condition, find unit vectors å and b or explain why no such vectors exist. (a) |a+헤-0…

A:

Q: Given vector a = 31 – 2j – yk and b= 3i- 2j + k. What is the value of y if a =b

A:

Q: Which of the following vectors are parallel to v = (6, 9) and whichpoint in the same direction?…

A: Given: v=6,9 and point in the same direction -24,-27

Q: Two non zero vectors a and b have respective magnitudes a and b , respectively. Given that c = a×b…

A:

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: if these vectors A = 4i – 2j + 4k and B = 4i + 5 j

A: we have ;  A→=4i-2j+4k ............(1)B→=4i+5j+0k  ...............(2)

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: Let the angle between two nonzero vectors u and V be 45°, the magnitude of the vectors be a and 2…

A:

Q: Use the Law of Cosines to find the angle a between the vectors. (Assume 0° < a < 180°.) v = 2i + 2j,…

A:

Q: Obthe resulting parallelogram from the following two vectors that form non-parallel sides A = 3 + 2…

A:

Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=ā and OT=b),…

A:

Q: Which of the following vectors are parallel to v = (6, 9) and whichpoint in the same direction?  (2,…

A: Let the 2 nonzero vectors be v and w and also the scalar vector be λ . Both the vectors are said to…

Q: Which of the following vectors are parallel to v = (6, 9) and whichpoint in the same direction? (12,…

A: Solution:Given     v=(6,9)To find the vector are parellel to v and point in the same direction.

Q: If U and W are unit vectors in R" and |U - 3W = v13, then the angle between U and W is: O a. 30° O…

A: Option C will be the right answer.

Q: If à = 2a, + 2a,y – a, and B = 3a, + 2a, – 6a, are vectors, find (a) Ả ·Ē (b) Ả × B (c) Angle…

A:

Q: Suppose a • b = -12 and b is a unit vector. a Explain why a and b are not perpendicular. b Given…

A:

Q: If a = 2i – j+2k and b =i+2j – 2k, find two vectors e and d satisfying all the following conditions:…

A: Let the required two vectors c and d be c=x1i+y1j+z1k and d=x2i+y2j+z2k. Now as per the given data,…

Q: For what values of a and b are the vectors 4= (2a-b, -1) and v (41 3a -b) equal ? write your ans…

A:

Q: nd the values of a for which vectors A and B are perpendicular where A = 2i+j+ ak and B = 2i+aj+k.

A:

Q: Let C and D be points with position vectors c and d respectively. If |c| = 5, \d| = 7 and c·d = 4,…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find the area of the parallelogram determined by the given vectors. 3 u = 2i – j+ 3k, v = ÷i + 2j –…

A: If vector a and vector b are the two adjacent sides of a parallelogram then the area of the…

Q: Given perpendicular vectors a = (5,3,-1) and 6=(2,2,k), find ||||.

A: Given perpendicular vectors a→=5, 3, -1,     b→=2, 2, k   To Find: b→

Q: Determine the angle between the two vectors: x = ai+bj+ck and y = di+ej+k where a = 2, b = 5, c = 1,…

A:

Q: If a and b are unit vectors in R', show that ||a x b||? + (a · b)² = 1. %3D

A: On solving this we will get:-

Q: A=2i+j+K Beitje ok Make twe Vectors Angle af magnitude @30 345

A: The formula to find the angle between two vectors is: θ=cos-1A·B|A||B|…

Q: Given the vectors u= 6i-2j and v=-i+9j, find 3u and u+v. Write your answers in the form ai+bj. 3u =…

A:

Q: ind the value of a so that vectors U = ai + 9j and V = 3i + 3j are

A:

Q: A ABCD is the parallelogram shown above. a) AC = BC + CD C Express AC in terms of any other vectors.…

A: We have to find out the diagonal

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

A:

Q: Use the Law of Cosines to find the angle α between the vectors. (Assume 0° ≤ α ≤ 180°.) v = 7i + 7j,…

A:

Q: Find the exact area of the triangle with two sides given by the vectors u = i+j- 3k and v = 2i…

A:

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

A:

Q: Two vectors are equal is they are parallel and have the same magnitude and direction ylgn O ihi

A: For two vectors to be equal, they must have both the magnitude and the directions equal.

Q: B side of cube = 10 cm (A. B); (C. D); (E.G);(G.B) ? (Ex F); (A x G) dan (Cx F) ? 2. what is the…

A: From the given figure we get A→ = 10i+10k B→ =10iC→ =5j+10kD→=5i +10kE→ =10i+10jF→=10kG→=10i+10j+10k…

Q: Which of the following pairs of vectors are perpendicular? /2 > and and and < - C. None of These…

A:

Q: Suppose that A = 2i + j, B =i- 4j + k, and Ĉ = j+k. What is the magnitude of the vector 2Ã –B + Č?…

A:

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: The angle that the x-axis make with the plane containing the following two vectors is A = 4â – 3 B =…

A: To find the angle

Q: Two non zero vectors a and b have respective magnitudes a and b , respectively. Given that c = a × b…

A: To show that,

Q: (The vectors A=i-j,B=j-k, and C = 3i-k, find triple dot (AXC). B

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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

A:

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

A:

Q: Q:: Find the area of parallelogram whose sides are a = 2i – 4j + 5k and b = i – 2j – 3k. Also find…

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.