2. Start with the vector -(2, 1) a) Rotate the vector 55° counterclockwise and sketch the resulting vector b) Reflect the vector =(2, 1) about the line x=y (which makes an angle of 45° with the positive x - axis) and sketch the resulting vector.

Q: Determine a vector equation for the line that is perpendicular to 7 = (4, 1) + s(−3, 2), sER, and…

A: We need to find the equation of line perpendicular to r→=(4, 1)+s(-3, 2),  s∈ℝ and passing through…

Q: Express the vector in terms of it's length and direction. i + 2j - k

A: Solution:Given   i+2j+kTo express in terms of its length and direction.u=vvand v=vu

Q: Find an equation of the plane that passes through the point (1, 3, −7) and is perpendicular to the…

A: Direction ratio of the line n=j is (0,1,0)  Given that the line is perpendicular to the plane.  So…

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

A: See the attachment

Q: what is the magnitude of the vector

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Q: I\ Find the unit vector that has the same direction as vector v = -4i - 3j + 6k ? %3D

A:

Q: As a result of losing a tug-of-war match, Mr. T is in the middle of a ditch. A group of people…

A: This question can be solved using the concept of vectors.

Q: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

Q: In the figure, a vector a→ with a magnitude of 24.1 m is directed at angle θ = 68o counterclockwise…

A: Given that: Magnitude of a→ =24.1mAngle of a→ w.r.t. coordinate axes: θ=68°Angle of primed…

Q: What is the vector between the point (−3a,−7b) and the point (−4a,−5b)?

A: Vector between two points A and B is B-A

Q: what is the vector equation of the line of intersection of the planes z=5 and x=9

A:

Q: If a 350-lb load is suspended by two chains as shown in the figure to the right. What is the…

A:

Q: 2. Start with the vector =(2, 1) a) Rotate the vector 55° counterclockwise and sketch the resulting…

A: Given: The vector x→=2,1. To find: a) the resulting vector after rotating the vector x→ by 55o. b)…

Q: Find the vector equation of the line that passes through point M(1, 1, 2), intersects the following…

A: Question is solved.

Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4 r=⟨ ,…

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Q: +C, vnere B 1s parallel to the vector (1, 2) C is perpendicular

A:

Q: Find a unit vector perpendicular to plane PQR determined by the points P(-3, 3, -4), Q(4, -1, - 23),…

A: Given query is to find unit vector perpendicular to PQR.

Q: If a 600-b load is suspended by two chains as shown in the figure to the right. What is the…

A: given  600 lb load is suspended by two chains

Q: A motorboat sets out at 10 am from a position (-6i – 2j) km relative to a marker buoy, and travels…

A: please see the next step for solution

Q: s the vector ở = (-1,–2,3) perpendicular to the plane 3x + 6y – 9z + 5 = 0? %3D

A:

Q: The vector from the origin to point A is given as (-2, -4, 5) and the unit vector directed from the…

A:

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

A: FORMULA

Q: Find a vector parametrization of the line through P = (3, -5, 7) in the direction v = (3, 0, 1)

A: Given:P=3,-5,7v=3,0,1

Q: A small plane is flying horizontally due east in calm air at 150 mi/hr when it is hit by a…

A: Let's find.

Q: In vector form, the equation of a line is given by r = (0, 1, 2) + t(2, 1,0), where t e R. T…

A:

Q: Find the orthogonal projection of the vector (2,4) about the line L parallel to the vector (-1,2)

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Q: Find a vector equation for the line through the point (2, 5, 8) perpendicular to the plane 2x + 5y +…

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Q: What vector has the same magnitude as the vector u = (4,-3) and points in the opposite direction?

A:

Q: o v based at the origin.

A: Sketch the vector v = (2, −3) based at P = (1, 4) and the vector v0 equivalent to v based at the…

Q: Find the equation for the plane through the point Po = (5,4,6) and normal to the vector n= 2i + 3j +…

A:

Q: a) Find the vector that is parallel to the tanget to the circle x2 + y2 = 100 at the point (3,-4).…

A: a) Given equation of circle, x2 + y2 = 100. We have to find the vector equation which is parallel to…

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

A:

Q: A vector is 0.888 m long and points in a 205 degree direction. Find the y-component of the vector.

A:

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

A:

Q: find the component form of the vector. The vector obtained by rotating [0, 1] through an angle of…

A: We have the vector is (0, 1)   We have to find the vector obtained by rotating (0, 1) through an…

Q: Find the vector of length 10 with the same direction as w = (2, V2, V3).

A:

Q: Find the vector of velocity which has a speed of (90m/sec) and parallel to the vector joining the…

A: Let Vector a is parallel to vector b then vector a = K Bn Where K is some constant and Bn is the…

Q: Explain why the vector 2u × 3v points in the same direction as the vector u × v.

A: Consider the vectors: u=x1i^+x2j^+x3k^v=y1i^+y2j^+y3k^

Q: i. What are the lengths of the x- and y-components of this vector? 10

A: Find your answer below

Q: Let u and v be vectors. If their dot product is zero what is the angle between u and v (in degrees)?

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Q: Find unit vectors Parallel to the YZ Plaane and PerPendicular to the Vector V = 51-j+2k ?

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Q: Suppose vectors u and v lie in the xy-plane (the z-component of each vector is zero). Now suppose…

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Q: Find the vector equation for the line of intersection of the planes 4x + 2y + 2z -1 and 4x + z= -2…

A:

Q: Assuming vector B is 12 units long, vector 4B is:

A:

Q: Find the equation of the plane passing through the point (2,−1, 3) and normal to the vector N = (2,…

A: we know that equation of plane which passes through point x1,y1,z1 and normal to vector a,b,c is…

Q: A vector has an x-component of −26.0 units and a y-component of 45.0 units. Find the magnitude and…

A: Explanation of the solution is given below..

Q: 2 A plane is flying on a course of 060° in still air at a speed of 300 km hr-', when it passes a…

A: Given that: Speed of plane = 300 km hr-1 Direction = Course of 60o

Q: Express the vector v = 4i + 2j - k in terms of magnitude and %3D direction.

A:

Q: Find the horizontal and vertical components of the vector u that has magnitude |u|=4 and direction…

A: Given that, the magnitude is |u|=4 and the direction angle is α=20∘