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

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

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

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Q: Find the area of the parallelogram that has the vectors u = ⟨3, −1, 5⟩ and v = ⟨2, −4, 1⟩ as…

A: Now

Q: Compute the angle between the vectors u = [2, 1, -2] and v = [1, 1, 1].

A: To find out the angle between two vector use the formula. First find dot product of these two…

Q: Find the vectors u and v whose initial point is u: (3, 2),v: (1, 4) and terminal points is (5, 6) ,…

A: Initial point is (3,2) and the ending point is (5,6) so the vector is u=(5,6)-(3,2)=(2,4)   Initial…

Q: Suppose that u and v are vectors in R' both of length 2/2 and that the length of u – v is also2 /2.…

A: The solution is give as

Q: Find the area of the parallelogram determined by the vectors: u = (1,0,–3),v = (2,3,0)

A: By using formula  Area of parallelogram

Q: Find the unit vector that has the same direction as vector v that begins at (1, 4, 10) and ends at…

A: We will find the unit vector that has the same direction with the given vector v in the following…

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

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

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Q: Find the angle θ between the vectors.u = (−4, 3), v = (0, 5), ⟨u, v⟩ = 3u1v1 + u2v2

A: Now,

Q: Find a vector that is orthogonal to the triangle with vertices P=(1,0,0), Q= (0,2,0), R=(1,1,1)

A: RECALL: Orthogonal vector:  Let us consider to vectors a→ and b→ then , cross product of a→ and b→…

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: For the vectors u=−1,4 and v=−4,2​, calculate projvu and scalvu.

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Q: Find the vector with length V17 and same direction as = (7,0, -6).

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Q: The unit vectors normal to the vectors (2, - 8,11) and (- 3,0,5) are

A: Find unit vector

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

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Q: Compute the distance between the vectors u = and v = 315

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

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

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Q: Suppose e vectors. that a and b ave nonzero Under what ciraumstarces is comp= compas Under ahat…

A: According to the problem, we have

Q: What is the length of the vector (1, 4, 5, -3) in R^4?

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Q: Find two unit vectors orthogonal to both u→=⟨3,4,1⟩ and v→=⟨0,3,3⟩.

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Q: u * v =( u1v1, UzV2 , Uz V3 , · Un Vn).

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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: For the vectors u= (-8,0,3) and v= (1,3,-3), calculate proj,u and scalvu.

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Q: Show that the vectors 3 do not span R° by giving a vector not in their span.

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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: Express à = (3, 1, –1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

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Q: Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z.…

A: The equation of a line that passes through the point x0 , y0 , z0 in three dimensional space is…

Q: ) Find a unit vector with the same direction as (1,0, 7).

A: We can find the unit vector as below.

Q: vector that is orthogonal to both u and v. u  =      v  =   <15, −18,

A: Given vector u→=-8,-6,4                    v→=15,-18,-1Now , u→ x v→=i∧j∧k∧-8-6415-18-1u→ x…

Q: The volume of the parallel pipe formed by three vectors A, B, and C is 50 cubic units. if A(-2,6,3),…

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Q: For each pair of vectors, calculate projvu and the vector component of u orthogonal to v. (a) u =…

A: Vector components

Q: Compute the angle between the vectors u = [2,1, -2] and v = [1, 1,1].

A: Given: u=21-2   and   v=111 Formula Used: cosθ=u.vuv

Q: If u, v are vectors such that |u || - 3, ||v|| - V5, and u v- 1, what is |u + v|| ?

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Q: a. From the set of vectors{ (1, 2, –1). (-4, –5, –6), (4, 3, 10). (5, –3,2)}. select two pairs of…

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Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0) Which axis on…

A: From the given points we can find two vectors and after that, using the fact that if one vector is…

Q: The vector from the origin to point A is given as 6ax – 2a, – 4az, and the unit vector directed from…

A: Given vector is A→=6,−2,−4 and B→=B23,−23,13 And B−A=10 We have to find the coordinates of the point…

Q: Find a unit vector that is orthogonal to both u = (2, -8, 6) and v = (4, 10, -6).

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Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (2, −1, 0), v = (−1,…

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Q: For the vectors u = (-5,0,3) and v= (1,4,-4), calculate projyu and scalyu. projyu = scal,u (Туре an…

A: The given vectors are u=(-5,0,3) and v=(1,4,-4)

Q: Consider the vectors ā (2, 3, –1) and b = (4, –9, 6). Find the cross product of a and b

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Q: Find the area of the parallelogram spanned by the following vectors. u = [4, –6, 5] v = [0, 6, 8]…

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Q: Find a unit vector u in the direction of v. Verify that llull=1 v=(-5,-3)

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

A: Here I am attaching image so that you understand each and every step.

Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis on…

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

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