1. Let the vectorsd (4,-3,4),5 (2,2,1). Find the projection of dontob. %3D %3D

Q: Which of the following is the vector projection of (1, 0, 1) onto (-2,4,0)? 1 B. (-1,2,0) C.…

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Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

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Q: |Given the vectors a = (1,2, 3) and b = (1, –1,2), what is the dot product a - b · a? 4 5 14 (7, 1,…

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Q: 10. Given two vectors u = [6,2] and v=[-2,1], determine the projection of u on v.

A: #10

Q: Find the vector projection of b = 6î + 3ĵ + 2k onto å = î – 2ĵ – 2k.

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Q: Suppose we have the triangle with vertices P(1,5, 1), Q(-4, 10, –1), and R(6, –3, -1). Answer the…

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Q: Let u (a, b, c) and v = (4, 5, 6). If u is parallel to (1,0, –1) and the projection of u along v is…

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Q: (d) Let u, v, w be arbitrary vectors in R³. What does the set of all combinations, Cu + c2v + C3w,…

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Q: When do directed line segments in the plane represent the same vector?

A: Vectors are represented by the line segments in which the length of the line segment is called the…

Q: 10. Given two vectors u = [2,4] and v = [6,2]. determine the projection of u on v.

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Q: Write the projection of 2î +3j-k along the vector î+j.

A: Given that: 2i+3j-k along the vector i+j.

Q: Given the vectors a = (1, 2, 3) and b = (1, –1,2), what is the dot product a · b · a? 4 14 (7,1, –…

A: a=(1,2,3)  and b=(1,-1,2)a.b.a  is dot product of three vectors

Q: Find the vector projection of OA = (4, 3) on OB = (4, −1).

A: This is a basic vector problem

Q: For what values of m and n are vectors [m,n,1], [2,1,3] and [2,1,1] coplanar?

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Q: Suppose ū = (0, -2, –1) and ū = (-4,0, 5). Then: 1. The projection of u along v is 2. The projection…

A: Need to find projection

Q: Let u = (a, b, c) and v = (8,9, 10). If u is parallel to (1,0, –1) and the projection of u along v…

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Q: ±). 1.4 Use vectors to decide whether the triangle with vertices P(1,–3,–2), Q(2,0, –4) and R(6, –2,…

A: solution of the given problem is below ...

Q: Given the vectors: A = 7+7+ k and B= 47+ 27+ k Find the vector projection of A onto B: Proj. _, A

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Q: Find the magnitude of the projection of (8, – 2) onto the vector (4, 7)

A: Wr have to find the magnitude of the projection.

Q: Below is a diagram of the dotted cube with edges of length 3. Suppose vectors u = (3,0, 0), v = (0,…

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Q: given the following points: A(3,-2,0) B (4,5,2) C (-3,2,1) Determine the vector projection of…

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Q: 2. Use a directed line segment to represent the vector. (а) и %3D (2, —4) (b) v = (2,4, –4)

A: Given that the vector a u=2,-4  b v=2,4,-4Solution a u=2,-4u=22+-42u=20  =25b v=2,4,-4v=22+42+-42v=6

Q: Find a vector a with representation given by the directed line segment AB. A(5, 4), B(0, 8)

A: We have to find a vector a with representation given by the directed line segment AB.

Q: Let a = (- 2,1, – 5) and b (– 3, 5, – 4). Find the projection of b onto a. Write an exact answer,…

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Q: Let a point a = (2, 4, 5). %3D Find a unit vector (just one) that is orthogonal to a.

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Q: Let ā = (1, – 5, 2) and b = ( – 1, 5, 3). %3D Find the angle between the vectors (in degrees).

A: We know that for two vectors a→ and b→,   cos(θ)=a⇀.b⇀|a||b|⇀⇀ where θ is the angle between vectors.…

Q: if vector AB =(-7i+3j+8k) and the point A= (-2,-2,6) find B

A: Given, AB =(-7i+3j+8k) and the point A= (-2,-2,6) Let the coordinates of B be (x,y,z) Now, AB = B-A…

Q: Find a vector perpendicular to d = [5,–4,6] and h = [-1,3,9].

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Q: Suppose we have the triangle with vertices P(1,6, 1), Q(-3,7,–3), and R(5, 1, 1). Answer the…

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Q: In R, evaluate the alternating 2-form 5 = -3 · dx A dy on the pair of vectors (a, b) if a = (4, 2,…

A: In ℝ3, we have to evaluate the alternating 2-form ξ=-3·dx∧dy on the pair of vectors (a,b). a=4,2,12…

Q: The following three vectors are coplanar: (3,5,6), (6,10,12), (-3,-5,6) True False

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Q: Which of the following vectors is coplanar to [1, 1, 1] and [1, 2, 3]? O a) [4, 2, -2] b) [5, 7, 6]…

A: Given vectors  [1,1,1] and [1,2,3] For coplanar with another vector, the determinant should be zero.…

Q: Given: a = (-1,-2,2),b=(3,3,4). Find the vector projection of b onto a.

A: Vector projection on b onto a

Q: Find two linearly independent vectors perpendicular to the w 41 -6- 1

A: Given: vector is v→=4-91 we have to find the two linear independent vectors perpendicular the given…

Q: 5 Given that p andr , find in column vector form: 4 p-r ep-2

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Q: Given the vector component of D(2, − 6, − 5) and G(1, 2, 3), find the vector of D that is parallel…

A: Given:      D2,-6,-5       G1,2,3 Two vectors D and G are said to be parallel if their cross product…

Q: Suppose that A, B, and C are vertices of a triangle and that a, b, and c are, respectively, the…

A: Let A=(x1,y1,z1)B=(x2,y2,z2)C=(x3,y3,z3)

Q: In R, evaluate the alternating 2-form 5 = -3· dx A dy on the pair of vectors (a, b) if a = (4, 2,…

A: Given that, ξ=-3.dx∧dy on (a,b) Where a=(4,2,12),b=(-7,-4,8) The objective is to show that ξ(a,b).

Q: 8. If the vectors in the figure satisfy |u| = |v|= 1 and u + v + w = 0, what is w ? u W V

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Q: Let ā = (3, – 2, – 5) and b (3, – 1, 1). - 1, Find the angle between the vectors (in degrees).

A: The angle between the vectors a and b  is given by:

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: A vector collinear to ū= is: a. d. 1,-2,-3> b. -1,2,3 > e. [K C.

A: Solution is here

Q: For what value(s) of a are the following vectors linearly independent: (1,5,-2), (0,6,a) and…

A: The vectors are linearly independent if the matrix formed from these vectors has non zero…

Q: - ()--)- 1 Let a = 2 and b = be two vectors. What is Jal2|b|2 - |a · bl2 ?

A: Here,  Given that  two vectors  . So, we find the value of  |a|^2.|b|^ - |a.b|^2

Q: ) Below is a diagram of the dotted cube with edges of length 5. Suppose (5, 0,0), v = (0, 5, 0), and…

A: Given u=5,0,0v=0,5,0w=0,0,5

Q: Determine whether the following three vectors lie on the same line in R?: и, 3 (4,6,8), и, %3 (2,3,…

A: The given vectors lie on the same line. u2=2,3,4u1=4,6,8=2×2,2×3,2×4=2×2,3,4=2u2So, u1=2u2Thus,…

Q: 4.15. Given vectors u = and v =, find the projection of u onto v.

A: Proceed as shown below...

Q: the vector from P1(1, 3) to P2(4, –2) is

A: Given :

Q: et x = [7, -4, -8] and y = [-6, -6, –10] be vectors in R'. Compute the following: %3D a+y [ -8x = […

A: Let's find.

Q: If ả = 2ỉ + 33, b = j – ỉ and ở = 33 are vectors in 2D, then determine the of a + 3b + c

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.