and = Wnte Pas the sum of two orthogonal vectors, 2 in S panƐu} and orthogonal to .

Q: Are vectors (금 ) and (금, 1, 금)' orthogonal? Justify. V3

A:

Q: Express EC by combinations of the vectors a, b and 7.

A: We have to write EC vector in terms of a,b and c

Q: 'he sum and difference of two vectors à and B are equal in magnitude. Prove lgebraically that the…

A: Given: A→+B→=A→-B→ The magnitude of sum of A →and B→ is , A→+B→=A2+B2+2ABcosθ The magnitude of…

Q: Find two vectors v1 and v2 whose sum is (-5, –5, 5), where vi is parallel to a =(0, –1, –2) while v2…

A:

Q: Eind vnit Vector that is ortogone a O u=(!,-!,2) and V=CO,3,1)

A: Here we have to find the unit vector orthogonal to u=1,-1,2 and v=0, 3,1

Q: Find the angle between the vectors a=(2,2,-1) and b=(5,-2,3)

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Q: For the vectors u= (-3,0,4) and v= (1,3, - 3), calculate projyu and scal, u. proj, u = OOD

A:

Q: Two vectors are considered equivalent (equal) vectors if they and

A: Every vector quantity has dimension as well as mangnitude.

Q: Find two unit vectors parallel to (2, 3).

A:

Q: 3. Find a unit vector with the same direction as (3, 4).

A: If we devide each component of vector v by |v| we will get the unit vector Uv.

Q: Are vectors v = ⟨ − 2 , − 3 ⟩ and u = ⟨ 6 , − 4 ⟩ orthogonal? Yes or No:

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Q: Find the angle between the vectors u = (-3,1,–2) and v = (-7,-5, 2) %3D

A:

Q: Let a and b be two vectors such that Jal =17, b is a unit vector, and 0= " is the angle between…

A: Solve for

Q: find the components of the vector PQ. P = (-}, 3, 1), Q = (4, 6, 0)

A: P=-12, 92, 1,  Q=4, 6, 0

Q: The length of the cross product between the vectors j and -j is equal to the zero vector. Select…

A: Solutions

Q: 4. If d and bare unit vectors and |a + 61= v3, determine (2d – 38)- (+2). %3D

A:

Q: Find a unit vector in the direction of u = (3, 4, 5).

A: Given vector, u=3, 4, 5

Q: find the diJ tance betueen the vectors

A:

Q: For the vectors u = (-1,4) and v = (-2,2), calculate proj, u and scal,u. projyu =

A:

Q: What us the midpoint between vectors: A = [3,4,5] B = [1,-1,1]

A: To find the midpoint of the vectors A = [3,4,5] and B = [1,-1,1] We have, x1=3, y1=4, z1=5, x2=1,…

Q: Find the measure of the angle between the three-dimensional vectors a and b. Express the answer in…

A: SOLUTION: given vector a=19, -1, 4 and b=1, -1, -5 to find angle between two vectors lets use dot…

Q: are the vectors u=(-4,2) and v=(-1,2) orthogonal, parallel, or neither?

A:

Q: 2. If a --i+3j-k and E-2itj-3K decompose vectoes E into the sum of two vectors, one is paralled and…

A: This question can be solved using the concept of condition of two vectors to be parallel and…

Q: Determine which of the vectors is parallel to z and which is orthogonal to z if z = (3, 2) Show work…

A:

Q: For the vectors u= ,0,2) and v= ,- 3), calculate projyu and scal, u. projy u = O DD

A: Given ,the vectors u=-4,0,2  and   v=1,3,-3

Q: Find the unit vector parallel to the sum of the vectors a [2, 4, -5], b = [1, 2, 3]. a.

A: Two given vector are ; a= 2i + 4j - 5k b= 1i+ 2j + 3k Resulting of vector a  & vector b  R= a+ b…

Q: What is the magnitude of the vector (2, 4, –4)?

A: FORMULA

Q: For the vectors u = (- 1,3) and v= (- 4,2), calculate proj,u and scal,,u. proj,u = ( -2,1) scalyu

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Q: Show that the pair of vectors is perpendicular. 3? + ? and ? − 3?

A:

Q: Find the smallest positive angle between the given pair of vectors. (3,1) , (4,6)

A: The given pair of vectors are,

Q: Find the angle between the vectors u and v if u = (2,3,5) and v = = (1,–4,3) in

A: First we convert this into vector then find the angle

Q: Find the area of triangle with the vectors p(0,1,4),0(-5,9,2) and R(7,2,8)

A:

Q: 6. Find the unit vector in the same direction as v. If u = (-12,8) and v = (-5,-12), find:

A: Consider the vectors u=<-12, 8>,    and    v=<-5, -12>. Need to find the unit vector in…

Q: Find two vectors v1 and v2 whose sum is , where v1 is parallel to while v2 is perpendicular to . v1…

A:

Q: 2. The unit vector in the same direction as (-6, 12) is

A:

Q: 10. Which of the vectors U =, V = and W = are in the same plane?

A:

Q: 1 If vector is a unit vector, what is the x?

A: We will find the value of x as following.

Q: Find the indicated vector. Let u - (-3,-7) --8, -1). Find -2u - 3v.

A: To find -2u-3v :

Q: Find two unit vectors orthogonal to a=⟨5,2,4⟩ and b=⟨5,0,4⟩ Answer so that the first vector has a…

A: We need to find a vector c→ , such thatc→ ⊥ a→ and c→ ⊥ b→ie,c→.a→ = 0  and c→.b→ = 0given,a→ = 5 i…

Q: Find the angle between the vectors u and v if u (2,3,5) and v = : (1,–4,3) in (Ctrl) ►

A:

Q: Show whether the vector w is a linear combination of vectors v1, v2 and v3 where --I --E --4 -- w =…

A:

Q: Determine the angle between the vectors a = (4, 5, 2) and b = (-3, 6, 0)

A:

Q: The distance between vectors v1 = (2, 1, -4) and v2 = (1, -1, -2) equals: Select one: O a. -2 O b. 3…

A: To find The distance between the two vectors v1=(2,1,-4) and v2=(1,-1,-2)

Q: OL a, b are the vectors Iedtenmined by tuoo adjacent Sides et a regular hexagon, what are the…

A:

Q: Which of these vectors is equivalent to the vector that has initial point (5,-2) and terminal point…

A: We have to find which of these vectors is equivalent to the vector that has the initial point (5,-2)…

Q: Verify that the vectors a = (2, 5, –1) and b = (3, –1, 1) perpendicular. а. are

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Q: a) tor which values on a are the vectors 87 2 -- a linearln independent?

A:

Q: 4. Find a unit vector that is perpendicular (5, 6). to

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.