3-6 . Vectors in Component Form Find the vector v with ini- tial point P and terminal point Q. 3. Р(1, —1, 0). О(о, - 2,5) 4. Р(1, 2, —1), 0(3,-1, 2) 5. Р(6, — 1, 0). 0(0, -3, 0) 6. Р(1, — 1, -1), Q(0,0, — 1)

Q: *₁ = (1, 2, 3), 2 3. Find the angle between the two planes 3x + y + z = 4 and 2x + 3y + 2z = 3 using…

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Q: 13. Find a vector equation of the line through (2, 1) parallel to (x, y) = (-2,7)+t(3,5). 14. Find a…

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Q: Three vectors are defined by position vectors defined m=(5,4,2), n=(-1,-3,6) and p=(x,-y,-z), where…

A: We have to calculate the following vector.

Q: 4. Use vector methods to find (a) the area of the triangle ABC where A(-2, -1, 1), B(3,-2, 1) and…

A: (a) Given vertices of the triangle are A(-2,-1,1) , B(3,-2,1) and C(1,3,-2)

Q: 4. (a) Find the unit vector that has the same direction as (3,4,0). (a) Calculate the distance…

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

Q: 6. a) Express as a linear combination of the standard basis vectors i and j the vector that starts…

A: Given query is to find the vector and it's magnitude.

Q: 13. (а) What is a unit vector? (b) and 6 = (2, –2,3). Determine the components of a unit vector that…

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Q: Find a nonzero vector u with initial point P(2,-3,6) such that (a) u has the same direction as v =…

A: Given: A non zero vector u with initial point P(2,-3,6) To find:  (a) u has the same direction as v…

Q: 17. Let a be a standard-position vector with terminal point (-2,-4). Let b be a vector with initial…

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Q: 2. Two soccer players are practicing for an upcoming game. One of them runs 10 m from point A to…

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Q: 4. Prove that the vectors a= (1,1,1); b-(1,-1,0) and e-(-1,-1.2) are orthogonal to each other! 5.…

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Q: The coordinates of the vector x= (7,5, – 16) in the basisB={v=(-1,0,3), u=(0, - 5,2),w=(2,0,1)} are:…

A: Given that x=(7,5,-16) and the basis is      B={v=(-1,0,3),u=(0,-5,2),w=(2,0,1)} . Here we have to…

Q: The plane passing through the three points A(4, –3, –4), B(-4, –3,2) and C(-3,3, –2) can be…

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Q: i,- (0. 금·금·0). 화 ( Also, let W-C(li, ia) and %3D Let the vectors ü = (40, 5, 40, 25) E R*. So, the…

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Q: 3. Find a vector equation of the line that... a) passes through (-3,5,-2) and (7,-3,1) b) has…

A: vector equation of line

Q: 1. Find vector, parametric and symmetric equations of the line containing the point P and parallel…

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Q: a) Find the vector orthogonal to the plane through the points P(2,-3,4), Q(-1, -2, 2), and R(3,1,…

A: equation of sphere centered at (h, k, j) and with radius R is: (x-h)2 + (y-k)2 + (z-j)2  =  R2 if A…

Q: 1. Find the vector component of the vector ū (-3, 6, 2). [28, 63, 0] in the direction of = %3D

A: We have to find vector component of u =[28, 63,0]  along the direction v=[-3, 6,2] Vector component…

Q: 1. Find a unit vector perpendicular to the line passing through the points (1, 0, -3) and (2, 1,…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: 3–8 - Cross Products For the given vectors u and v, find the cross product uX v. .3. и %3D (1,0,…

A: 3).  Given u=1,0,-3, v=2,3,0. To find the cross products. Solution: Finding cross products of given…

Q: 1 Find the vector equation of the plane given by two vectors u and v and one point P: a u=1…

A: The vector equation of the plane is of the form: xi→+yj→+zK→=0 a. u=214, v=-12-1,P=(0,2,-1)…

Q: The coordinates of vector x = (3, -2, 4) relative to basis B = { (0, -3, 4) , (1, 0, 0) , (O, 4, 3)…

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Q: 4. Find an initial point P of a nonzero vector u = PQ with terminal point Q(3,0,–5) and such that u…

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Q: 27. Given vector v with initial point (16, -30) and terminal point (-22, -10), a. Find the component…

A: Given: A vector whose initial point is 16, -30 and terminal point is -22, -10.

Q: 9. Given the vector ū =[-2,3,–4] a) Draw the vector. b) Determine a unit vector collinear with ū. y

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Q: 19–22 - Sketching Vectors Sketch the given vector with initial point (4, 3), and find the terminal…

A: (19)We can write the vector asv=<x2-x1,y2-y1>Where R(x2,y2) are the coordinates of its…

Q: 7-10 - Terminal Point of a Vector If the vector v has initial point P, what is its terminal point?…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: 5. If we have two vectors (V₁ and V₂), V₁ is a vector perpendic through the points A(1, 2, 5),…

A: Introduction: When a vector is along the direction in another vector, the two vectors are parallel…

Q: 7) Find a vector that is orthogonal to the plane that contains the points P(1,–2,4), Q(-2,3,2), and…

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Q: 1-4 - Operations with Vectors Find u|, u + v, u - v, 2 u, and 3u - 2 v. 1. u = (-2, 3), v= (8, 1) 3.…

A: 1). Given vectors are u=-2,3, v=8, 1. To find: u, u+v, u-v, 2u and 3u-2v. Solution: We have u=-2,3…

Q: (1 point) Find a vector equation for the line segment connecting the points P = (-9, –8, –1) and Q =…

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Q: 2. Given the points X(-3, -1, 5) and Y (4, 4, -9): A. Write the position vector OX in vector form:…

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Q: Two soccer players are practicing for an upcoming game. One of them runs 10m from point A to point…

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Q: 19. Find two unit vectors orthogonal to both (3, 2, 1) and (-1, 1, 0). Answer

A: Unit vector orthogonal to both a⇀, b⇀ is: ±a⇀×b⇀a⇀×b⇀

Q: ransform the vector A = 3i – 2j – 4k at P(2,3,3) to cylindrical coordinates

A: For the vector given by xi+yj+zk. For the cartesian coordinates P(x,y,z),the corresponding…

Q: 1) The orthogonal vectors u and V of the following are a) u = (1,0,1) and v= (0,1,1) b) u (3,0,-1)…

A: solution:-(1) for orthogonal vector u·v=0(a)u·v=1,0,1·0,1,1=1×0+0×1+1×1=1  not…

Q: Find a vector equation of the plane containing the points ?(2, 0, −1), ?(3, 4, 0), and ?(4, −1, 1).

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Q: 4) The distance vector form the point (2, n/2 ,1) to the point (4 , n,3) is: a) -бау + 2аz b) 3(v3 -…

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Q: 1. Find the unique unit vector ī = (v1, v2, v3) that is orthogonal to (1, 1, –2), forms an angle of…

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Q: (-34,-9)and terminal pointQ-14 Given a vectorv with initial potnt the unit vectorstand i.

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Q: (5) Find the vector equation of the line that passes through the point (1,5) and is parallel to the…

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Q: 5. Let u be the vector with initial point (2,0) and terminal point (3,2). Let v be the vector with…

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Q: 8. a. Using the vectors x = (3, 3, 1) and y = (-−1, 2, -3), verify that the following formula is…

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Q: 1. If vectors u (3, 3), v-( 13. -7), and 2w +3u-v%3(4,-4) what is the coordinate of vector w?

A: Topic = Vector

Q: 7. (a) Let v be a vector with initial point (-1, 4) and terminal point (3, -2). Let w be a vector…

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Q: (3, -1, -3) of the vector with components (2, -8,2) ii) Find the projection vector on the vector v =…

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Q: 1. Find all unit vectors that are parallel to the line going through the points (1, 3, – 1) and (2,…

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: Example 2: Find the unit vector in the direction of v = (-1,3,4) and verify that this vector has…

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Q: a linear combination of the vectors Can we express the vector a = (2, – 5, 3) as e = (1, 1, 1), ez =…

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