Chapter 11, Section 11.2, Question 025c Find the component form of the vector v in 2-space that has the length and makes the angle with the positive x-axis. v =( ? Edit ? Edit

Q: If         →                    AB = (−5, 4) then 4 is the _____ of the vector.

A: We know in a vector of the form (a, b); a is the x-component and b is the y-component of the vector.

Q: Chapter 13, Section 13.6, Question 033 Find Vz. z = sin (8y – 4xy) Give your answer in unit vector…

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Q: Suppose and are non-zero, parallel vectors. Which of the following could not possibly be true?

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Q: A turtle starts at the bottom left corner of a garden [point (0, 0)], and moves according to the…

A: Given turtle and its moves point

Q: 2- Suppose that vector v has initial point (-4,5) and terminal point (-1,12). a- Find the component…

A: a)A position vector v→ is defined as a line extending from the initial point (x1,y1) to the final…

Q: The unit vector in 2-space that makes an angle of π/3 with the positive x-axis is _____

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Q: Find a vector a that has the same direction as (-8, 5, 8) but has length 3. Answer: a =

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Q: 6) (Section 9.4) Given u = then иnit vector in the a direction of и is

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Q: Sketch the given vector with initial point (1, 6). u = (-7, -4)

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Q: . Show that the vectors = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

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Q: Find the vector in the direction of (5, – 12) with length 3.

A: To find: A vector in the direction of 5,-12 with length 3.

Q: Under what circumstance is the scalar projection of u onto v equal to the scalar projection of v…

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Q: Find the length of the vector a %3D

A: The length of a vector x→=abc is given by the equation; ||x→||=a2+b2+c2

Q: 11) (Section 9.5,9.6) Find a unit vector that is orthongonal to both u and v. u= (2,-1,3) v=(1,0,–2)…

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Q: Find the vector from the origin to the point of intersection of the medians of the triangle whose…

A: To determine the point of intersection of the medians of the triangle.

Q: 2) (Section 9.4/9.5) Determine the value of 'a' that would make the vectors perpendicular u = and v…

A: For the vectors to be perpendicular  Then the dot product of two vectors is zero.

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: Find a parametric representation of a straight line passing through (1,2,1) in the direction of…

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Q: Give an example of a non zero vector that is perpendicular to (5,7,4)

A: We know that "two vectors are perpendicular to each other if and only if their dot product is zero"…

Q: Construct a geometric figure that illustrates why a line in R2not through the origin is not closed…

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Q: Find the magnitude of the projection of (– 5, – 7) onto the vector (– 8, - 4)

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Q: Sketch the given vector with initial point (4, 1). u = (-5, 3)

A: Here we have to plot the given vector.

Q: 9) (Section 9.4) Find the magnitude of vector u = -60i+11j

A: Given,   u = -60i+11jMagnitude of vector ; u=-602 + 112u = 3600+121  = 3721 =61

Q: 6. A student claims to have found a vector A such that (2i - 3j + 4k) x A = (4i + 3j - k). Do you…

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Q: Find the length of the vector. v = (-2, 0, 5, 1) %3D ||| M = %3D

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Q: 7. Give the terminal point of the position vector of ü= (3,4). Clearly show why %3D your answer is…

A: Concept: A vector is a directed line segment with an initial point and a terminal point. Vectors are…

Q: Give an example of vectors in R^3 that spans R^3. (show works)

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Q: What is the vector projection of X = (7, 0, – 3) on ỹ = (-1,3,3)? Answer:

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Q: Sketch the given vector with initial point (7, 5). %3 (4, 2) u =

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Q: A vector w has initial point (1, -5) and terminal point (-2, -3). Write w in component form.

A: We find the vector in component form when the initial and terminal points are given by simply…

Q: five vectors in Span v1, V2}. Do not make a sketch. 8 - -

A: In this question, the concept of the span of the vector is applied. Span The smallest linear…

Q: Let a point a = (2, 4, 5). Find a non-zero vector (just one) that is orthogonal to a.

A: We say two vectors are orthogonal if they are perpendicular to each other .i.e. the dot product of…

Q: Let ū = (3,2), v = (-2, –2), and w = (-4,3). Find the vector x that satisfies 5u – v +x = 7x + w. |…

A: Given that u→=3,2v→=-2,-2w⇀=-4,3

Q: Find the length of the vector. v - (9, 12)

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Q: Project the vector b = (1,3,1)" onto the line through %3D a13D (-1,2, 2)Т, (2, 2, –1)", аz 3D az=…

A: Given: Let us assume, b= (1,3,1)T  a1=(-1,2,2)T   a2=(2,2,-1)T   a3=(2,-1,2)T

Q: Chapter 13, Section 13.6, Question 033 Find Vz. z = sin (4y² – 5xy) Give your answer in unit vector…

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Q: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=<2,-2,1>.

Q: Find the angle between the vectors (-8, –7) and (-6, 4). Carry your intermediate computations to at…

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Q: (1,2,3) and Question 3. Evaluate the cross product of the vectors u = =(-1,0,2). Also evaluate (u ×…

A: Given u= <1,2,3> and v=<-1,0,2>  Find u×v and (u×v).v

Q: Show that the vectors (4-3) and (5,2) form a basis CF TR

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Q: Chapter 11, Section 11.4, Question 033 Use the fact that the volume of a tetrahedron with adjacent…

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Q: Section 2.5 in Volume 3 2. Find the equation of a plane that passes through the three points (1, 5,…

A: Given information:- Find the equation of a plane that passes through the three points (1, 5,3).…

Q: In Cartesian coordinates, the position vector at point (3, 40, 1) is represented by 2.29ax+1.93ay+az…

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Q: Section 2.5 in Volume 3 0) 3. Find the distance the point (4, 5, 2) is away from the plane 2a 7y+ z…

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Q: Find all vectors u that satisfy the equation (1,1,1)×u= (−5,2,3).

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Q: In Cartesian coordinates, the position vector at point (3, 20, 1) is represented by…

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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)…

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.