The initial point of two vectors is A(4, 4, 2) and the terminal points are B(2, 6, 3) and C(o, 4, 5). Determine: 1. The vectors AB and AC, and the unit vector for AB and AC. 2. AB + AC, 2AB + 3AC 3. AB AC, and the angle between the two vectors.

Q: Determine the angle between the given vectors. (а) а — 3і — 2ј, b %3 2i + 2j

A: a→=3i - 2jb→=2i + 2j

Q: For the given vectors: å = (-2,-3), = (1,-2), č = (2,3), find: (a) 3ã – 5 + 2č (b) angle between the…

A: Vector: A quantity that has magnitude, as well as direction, is called a vector. The magnitude of a…

Q: Given the following points A, B, C and D, which of the vectors and are parallel? CD (a) A= (1, 2),…

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 -6,-9 in the same direction

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

A:

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

A:

Q: If A = 4a, - 6a, + a, and B = 2a, + 5a,, find: (a) A B +2|B (b) a unit vector perpendicular to both…

A:

Q: Given the points A(1,2,3,) and B(2,-2,1) Find the Vectors A and B with respect to origin. Unit…

A:

Q: 8) Given the vectors (5, 5) & (5, -5); both vectors start at the origin, find "e", the angle between…

A: Vector is a quantity that has direction as well as magnitude. In coordinate system, length of vector…

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: c) The vector from the origin to the point A is given as (6, -2, -4), and the unit vector directed…

A: This is complicated problem.So I can do it in Advanced Mathematics.

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: 02. Given the vectors : A = (3.-1, 2), B = (0, 1, 1) and C- (2, 2,-1), find: the angles between the…

A:

Q: 6. Find the magnitude of the resultant of two vectors u and v, given u=2, y =7 and the angle between…

A: We have to find the magnitude of the resultant of two vectors and v and the angle between the…

Q: Two vectors (M = 4ax-bay) and (N = 6ax-2ay-Saz), find the vector perpendicular to these vectors?

A: Given Vectors are                                                 M=4ax-6ayN=6ax-2ay-5az vector…

Q: Consider the vectors ä = 5i+ 3- k, 6= 5i – 3 + k, 1+53+ 6k d = i+3+6k, j = -1-53+ k. Which pairs (if…

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: Given the points A(1,2,3,) and B(2,-2,1) Resultant, vector C, of vectors A and B (A+B) Vector AB

A: resultant vector C = A+B  = (1+2,2-2,3+1)  = (3,0,4)

Q: For the given vectors: å = (0,3), b = (4, –2), ở = (3,2), find: (a) 3å – 6+ 2č (b) angle between the…

A:

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: sketch the vectors −→AB and −→P Q, and determinewhether they are equivalent A = (1, 4), B = (−6, 3),…

A: Given, A=(1,4), B=(-6,3) P=(1,4), Q=(6,3)     Sketch the vectors AB→ and PQ→, and determine whether…

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: The angle between vectors (1,-1,–2) and (0,4, –3) is, approximately,: Select one: a. -1.41 O b. not…

A:

Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b, 1/2a +…

A: answer

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

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: A triangle in R3 has two sides represented by the vectors = (2, 3, –1) and OR = (1, 4, 1). Determine…

A: Topic:- vector algebra

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: (a) For the vectors d = (2, p, 8) and b = (q, 4, 12), determine values of p and q so that the…

A:

Q: Consider the points A=(1,2,3), B=(-2,1,0), and C=(0,3,1). Adding the vectors, find 2AB+3AC.

A: To find 2AB +3 AC

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: Given: 6j, -4i

Q: Two vectors are defined as A = ax + 2ay + 3az and B = 3ax + 2ay -7az . Which of the following vector…

A:

Q: Determine the angle, to the nearest degree, between each of the following pairs of vectors: a. d =…

A:

Q: For the given vectors: a = (2,–3), b = (0,3), c = (1,4), find: (a) 3å – 6+ 2č (b) angle between the…

A: a) this is the case of scalar multiplication and then addition and subtraction. So 3 times of vector…

Q: For what values of b are the vectors (–88, 6, 7) and (b, b², b) orthogonal? Answer (separate with…

A:

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: 10,7 and -2,-75

Q: Find the angle between the vectors v and w v = (−2, 3, 1)T , w = (1, 2, 4)T

A: Consider the given vectors: Here the objective is to find the angle between vector v and w.

Q: Find the dot product of the two vectors v= w= and the angle between the vectors.

A:

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 3. +-b and Aa…

A: We have to find the value of lambda by using the data given above

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 1 3, a +2b,…

A: The equation of the line PQ is : PQ=Q-P=12a+34b-(a+2b)=12a+34b-a-2b=-12a-54b The equation of the…

Q: For the vectors: (6, –5) and V = (-1,4) U = Which of the following is the correct value of: |3 7ỉ –…

A: Here we have to find |3u - 2v| using given u and v vectors

Q: Find the angle between vectors v=(1,1,1,-1) and u=(1,3,1,-1) ал Write the answer as a/b for the…

A: To find The angle between two vectors.

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: a) If u and v are two-dimensional vectors, we calculate the dot product as   u=(u, u2) and v=(v1,…

Q: Given the two 3-D vectors a=[-3, 4, -6] and b=[-1, 2, -1], find the dot product and angle (degrees)…

A: Consider the given 3D vectors.

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: Given the vectors a = (−2, −5, −3) and b = (1, −4, 2), find A unit vector in the direction of a.

A:

Q: For the given vectors: å = (1,2),b = (-4,3) find: (a) 3å – 45 (b) à -5 (c) Angle between the vectors

A:

Q: Given two vectors P = 9i + 9j + (-9k), Q = (-6j) The angle between the two vectors is

A: We have two vectors P=9i+9j-9k and Q=-6j. Then the angle between the two vectors.

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.