QUESTION 7 OA = 21 – j + nk , OB =i+3j – 2K The position vectors of points A, B and C are and OC = -i- mj – 3K , where O is the origin, m and n are constant. Find: i. m and n if BA x BC = – 16ỉ – 35 + 2K . ii. Using the value of m and n from (i), find LABC.

Q: 12 If the position vectors of P and Q are i+3j- 7k and 5i - 2j + 4k respectively, find PQ and…

A: Since,you have posted multiple questions so according to our guidelines we will solve only first…

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: 6) Find the x- and y-components of the vector ở with magnitude |ū] = 16.4 cm/s², and direction 0 =…

A: Here, magnitude is 16.4 Direction is 156.5°

Q: Question 01: Sketch the vectors ro = and v= and then sketch the six vectors ro±v,ro ± 2v,ro ± 3v.…

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Q: QUESTION 5 Consider the following four objects. () The vector (1,2,3) (i) |+ 2) + 3k (i) The vector…

A: The options i, ii, iii depict a vector <1, 2, 3> while the 4th option is just a point (1,2,3).

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: QUESTION 1. Three vectors are defined by position vectors defined m= (5,4,2), ñ=(-1,-3,6) and p =…

A: From the given problem:   m→=5,4,2 ; n→=-1,-3,6 ; p→x,-y,-z   From the scalar multiplication:…

Q: The position vectors of points A, B and C are OÃ = 2i – j + nk , OB =ỉ+3j – 2K and OC = -i – mỉ – 3k…

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Q: Question 2. Let ū = 31 – k, i = -ỉ - 3+ 2k. %3D (a) Find unit vectors in the direction of ū and ū.…

A: As per our guidelines we are allowed to solve one question at a time. Kindly repost the rest…

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

A: The given question is related to vectors. The solution is explained below.

Q: Question 1 a) Find the value(s) of y such that the vectors U₁ = and u₂ = are parallel. b) Find the…

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

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Q: Question 17 Write the vector v in terms of i and j whose magnitude Iv and direction angle 0 are…

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

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Q: Question 27 The position vector of a particle is r(t). Find the requested vector. The velocity at t…

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Q: Question 1: Given the points P(-9,6) and Q(3,12), state a UNIT vector in the same direction as PO

A: P (-9,6) and Q (3,12)PQ→ = [3 - (-9)]i^ + (12-6)j^PQ→ = 12i^ + 6j^PQ→ = is the vector joing (-9,6)…

Q: Question 5 Let u = 5i – j+k, v=j-5k and w=-15i+3j– 3k. Which vectors, if any, are a) Parallel b)…

A: Two vectors u and v are perpendicular if u.v=0                                        Parallel if…

Q: Question 1. (25). For the vectors u = 2i + j + 2k and i = i – 2j – 2k. a. Find u· ū, i ·ở and ū · Ữ.…

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Q: 12. If the position vectors of P and Q are i + 3j-7k and 5i- 2j + 4k respectively, find PQ and…

A: NOTE: Hi! Thank you for your question. As per the honor code we are allowed to answer one question…

Q: 21A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, and C = i-2j+ k, find (A x B).C

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Q: QUESTION 8 Consider the vectors u=(-1, 6, 4) and v=( -2, -4,-2). Find | -4u -6v |. (Type your answer…

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Q: QUESTION 1 Find the curvarure K of the vector position r(t) = %3D O A. B. Non of the above. O C. 1…

A: We need to find the curvature of the position vector rt→=2t , sint , cost The formula for curvature…

Q: Let v = (1, 1, 1) and w = (6, -5, 10). Find the cosine of the angle 0 between the vectors v and w.…

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Q: QUESTION 3. a) Three vectors are defined by position vectors defined as ā = 2i +j- 3k, b = -3i + 2j…

A: We need to find scalar triple and vector triple product  here i find answer in terms of x ,y ,z

Q: 3. Find the angles a, ß,y, which the vector Á = 3î – 6î + 2k makes with the coordinates axes and…

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Q: Question 2 For what value of t, if any, is the vector (4t, 1) parallel to the vector (4, -1) ? %3D…

A: We have to find the value of t.

Q: . Find the angle between the vectors å = 4i – 35 + k and b = 21 – k. (First find an exact expression…

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Q: 4. Consider the points A(1, –1, 4), B(2, – 2, 5) and O(0, 0, 0). (a) Calculate the cosine of the…

A: The given points are A(1,-1,4) and B(2,-2,5) and O(0,0,0) The cosine of the angle between two…

Q: 4. Find the angle between each pair of vectors. Round to two decimal places as necessary. a) (V3,…

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Q: Let i = 3i – 13j +k and j = 13i + 3j+ 5k be the two vectors. Find the angle (in radians) between the…

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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: Question 12 Write the vector v in terms of i and j whose magnitude v and direction angle 0 are…

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Q: Question 8 Express the vector u' below as a sum of two vectors lj and u,, where uj is parallel to…

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Q: If a line is parallel to the vector 4i + 1j + 4k and passes through the point P = (3, 7,9), then the…

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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: Q1A)The vectors A=i-j,B=j-k, and C= 3i-k, find triple dot (AXC).B . B)Convert = cos ¹(r-1).

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Q: Question 8 Relative to a fixed origin O, the points A, B, and C have the following position vectors…

A: The position vector can be represented in form of a column vector. The matrix operations and rules…

Q: If a line is parallel to the vector 8i + 5j+3k and passes through the point P = (6,2, 4), then the…

A: The line which is parallel to the vector  ai + bj + ck and passes through (x1 , y1 , z1) has the…

Q: Question 17 Let A and B be points with position vectors u and v such that [u] = 6, |v| = 8 and u v=…

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Q: QUESTION 7 The angle between the vectors u=-5i-8j and v=2j+k is degrees. (Calculate your answer…

A: Explanation:

Q: QUESTION 3. a) Three vectors are defined by position vectors defined as ā = 2i + j– 3k, b = -3i + 2]…

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Q: Let i = 47 – 107 + k and y = 10i +4j +5k be the two vectors. Find the angle (in radians) between the…

A: Given:

Q: 11.3.19 In the figure to the right, it looks as if v, + v, and v, - v, are orthogonal. Under what…

A: Dot product of two orthogonal vectors are always equals to "0" . Therefore, if v1+v2 and v1-v2 are…

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: (Question 1] Let A= p coN()a, +sin()a, +z'a, and B= xya, + y'a, + za, find 1. A•Bat (2, ", 3'6 2.…

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Q: QUESTION 1. Three vectors are defined by position vectors defined m= (5,4,2), ñ =(-1,–3,6) and =…

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Q: Question 1. Use the following information about some vectors in R to answer the questions following:…

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Q: A positron undergoes a displacement Ai = 2.02 – 3.03 + 6.Ok, ending with the position vector f3.0j -…

A: Any position vector, r→ is represented as r→=xi^+yj^+zk^ . Let two vectors be r1→=x1i^+y1j^+z1k^ and…

Q: Question 1 Let a = 2i − 3j + 2k and b = i − 2j – k. - Determine whether the vectors a a) and b are…

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Q: 4) If p = 6i+7j-2k and q = 31-j+4k, find: a) p x q b) the sine of the angle between vector p & q. c)…

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