1. Three vectors are given by: å = 2î – 3ĵ + 5k, b = -2î + 7j – k and č = lî + 2j – 4k. axb Find a, so that A: [2č] = -4. а. b. Calculate the angle between b and a position vector with coordinate (0, 0,-3).

Q: Q3:If the two vectors A= 3i +2j + 5k, and B= 2i - j+4k, they located in the x and y plane, find the…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 4) Given a = 2i + 3j + k , b = 3i – Sj + 9k and c the vector joining P1 (3, 4, 5) to Pz (1, -2, 3) ,…

A: The vector C is:  c→=1,-2,3-3,4,5    =-2,-6,-2

Q: Given vectors u=i+2j and v = 3i + yj, find y so that the angle between the vectors is 60°. roo…

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

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Q: (b) Find the angle between the vectors u and v if u = (2,3,5) and v = (1, -4,3) in %3D R3.

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Q: b) Consider the vectors a = 3i – 2 j +7 K, and b = -5 i +4 j-3 k, find 1- a.b 2- Angle between a and…

A: b Given vectors are a=3i−2j+7k and b=−5i+4j−3k. 1 We have to find the a⋅b…

Q: for what value of Ca) will the Vector ū = -41-8)4ak,ū =ei+4j-5k are parallel

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

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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: Find the angles between given vectors. (a) ā = 3i + 4j and b= 5i – 4j (b) a = 3i +4j - 5k and 5= 6i…

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Q: 3 Give the position vectors of A, B, C, D and E relative to O for the diagram below. B D-

A: In geometry a position vector so known as location vector. Here we find position vector relative to…

Q: The angle between the vectors i = î + 2î – 4k and w = 2î + 3ĵ + 5k is - obtuse. Select one: OTrue…

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Q: (1) Let 0 be the angle between vectors A and B, find the value of the angle 0 when

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Q: For what value of (a) will the vectors V=-4i-8j+ak, U=2i+4j-5k are parallel?

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Q: The angle between the vectors A = 17- 31+4 k and B= 5î -3ĵ+0 k, in term of cose is Answer:

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Q: Find the value of b so that vectors U = 5i +12j and V = 4i + bj are perpendicular.

A: Given :          U=5i+12jV=4i+bj

Q: 4 3 Let U 4 and V = - 5 - 3 -2. Find the angle between the vectors (in radians).

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Q: Q2: Find the angle between the two vectors A = 5i - j+ 2k and B = -3i + 2j + k

A: Angle between the vector u and v is θ=cos-1u.vu.v.

Q: 3. Given the vectors v = i- 2j – 2k and w = 31 – 5j + 4k, find (a) the cosine of the angle between i…

A: The given vectors are, v→=i-2j-2kw→=3i-5j+4k The magnitudes of the vectors are as,…

Q: If the angle between the vectors A = xâ, +â̟and B = /3â, +â, is 60°, find x.

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Q: Find cos(0) if 0 is the angle between the vectors u= 4i – 3k and v = 2i – 2j + k 2 14 15 15

A: First I have written a short note , just use them and find that  Answer is 1/3

Q: s given 2 vector A and B of non zero magnitude, what is the angle between them if A.B as value -AB/2

A: The dot product between two vectors, X and Y is defined by the formula, X·Y=XYcosθ, where, θ is the…

Q: Q.3 Find the cosine of the angle between the vectors: a = 2i-8j + 3k a =i+2j-k a = 4i + 2j-k b= 4j +…

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Q: = 3. 6. Find the magnitude of the resultant of two vectors u and v, given = 5 and the angle between…

A: Explanation of the answer is as follows

Q: Q3) If A -3i + 4J – 5k and B= 5i-6J +7k find the unit vector which is perpendicular to these two…

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Q: 2. If å and b are two vectors with lengths 2 and 5 and angles between 150°, respectively, obtain the…

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Q: Let v = (1, 1, 1) and w = (6, -5, 10). Find the cosine of the angle e between the vectors v and w.…

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Q: 4) Given a = 2i + 3j + k , b = 3i – 5j + 9k and c the vector joining p1 (3, 4, 5) to P2 (1, -2, 3) ,…

A: Given,  a→=2i^+3j^+k^ Also given c→ is the joining vector of p13,4,5 and p21,-2,3 Then,…

Q: Ã = ë, + 3ểy – 2ể, : Calculate the angle between the B = 4ëx – ëy : vectors A* and B". = -3e, - 5ẽ,

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Q: 3. Calculate the angle (degrees), between vectors p = 2i +9j – 4k and q = -3i + 5j + 6k correct to…

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Q: ) If m = 2i+2j-k and n = 31-6j+2k, find: a) m ·n and b) the angle between m and n. c) the component…

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Q: 1. Assume the lengths of the vectors 2a – b and å + 35 , assuming å = (2,1,3) and b = (-1,2,2) 2. If…

A: Using scalar multiplication of vectors and magnitude of vector concepts  we can solve this question

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: Q3: Find the angle between two vectors in space A = 41 – 2J – k and B = 4T – 2J + 4k (5 marks)

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Q: Q.3 Find the cosine of the angle between the vectors: a = 2i -8j + 3k a =i+ 2j-k a = 4i + 2j-k b =…

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Q: (1) Let 0 be the angle between vectors A and B, find the value of the angle 0 when |-5V3A x B = 5Ã.B

A: To find the angle θ between vectors A and B. It is given that,

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

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Q: Suppose that u and v are vectors in R' both of length 2V2 v is also? v2. Thenllu + v|| and that the…

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Q: -) THREE VECTORS A, B, AND C ARE RELATED AS FOLLOWS ! A AT 180°, A +C =-5+j15, 2 C = CONJU GATE OF…

A: Solution :-

Q: Given the vectors v = 3i-8j and w = 6i-j, find 5v and v+w.

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Q: 2a.) Suppose u, w are two vectors in R7 satisfying uxu 4, wxw 16, uXw = 8, What is the cosine of the…

A: We are given that : u→.u→=4⇒u→u→cos 0=4⇒u→2=4⇒u→=2 w→.w→=16⇒w→w→cos 0=16⇒w→2=16⇒w→=4 Now, Let θ be…

Q: Given the following vectors: di = 3î – 2j, d, = -5î + 2j – k What is (di + dz) · (dị × (4dz))?

A: d1 =3i-2j+0k d2 =-5i+2j-k

Q: In the diagram below, a and b are vectors such thay cos0 = 1/6. Given thay a= i +j+ pk and b= 2i…

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Q: (3) Find the angle between the vectors u= 2i-2j4tk and

A: given vectors are  u=2i-2j+k  and v=3i+4k find the angle between these vectors

Q: 2. Find the angle between the following two vectors. and

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Q: The angle between vector A =4ax+5ay+6az and B = 3ax -2ay + 4az is * O 68.75 degrees O 56.62 degrees…

A: Angle between two vectors

Q: Here is a drawing of vectors a, b, and c. 18 ć Which equation correctly describes a in terms of b…

A: Given drawing of three vectors.

Q: If A = 3i + 4j and B = 7i + 24j, the %3D vector having the same magnitude as B and parallel to A is…

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Q: Q3: Find the angle between two vectors in space A = 41 - 2J-k B = 4T - 2J + 4k and

A: We need to find the angle between vectors A=4i¯-2j¯-k¯  and B=4i¯-2j¯+4k¯ for this we will use the…

Q: b) For what values of A, the vectors 2i -j+ 2k and 3i + 22 j are perpendicular?

A: If we have two vectors ai^+bj^+ck^  and a'i^+b'j^+c'k^ , then, these vectors are said to be…

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.