Prove that planes a-y+3z - 2 0 and 2x 4y-2z-7=0 are crossing via the line L. | %3D Find the direction vector 3 of line L, that forms an acute angle with OY-axis and has length /66. Evaluate the acute angle o between the planes. n Answers: • Direction vector of L: • Angle between planes: (degrees).

Q: The path of a particle is moving in the plane with position vector . What is the speed of the…

A: position vector given <sin2t , cos5t> speed = ?    at   t =2

Q: A straight line has vector equation given by r=(1-A)i+(3+2A)j.How far is this line from the origin?

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Q: Vector A is 35 m long and makes an angle of 60° clockwise from the positive Y-axis. Vector B is 55m…

A: We have given a vector A of magnitude 35 m and makes angle 60∘ from the positive y-axis i.e. 30∘…

Q: ) Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A: Given problem:- Find the vector that parallel to the intersection line of two planes 2x + y - 3z = 2…

Q: Show that the lines L₁ : x = 4-t, y = 2t, z = 1+ t and L₂ : x = 1 + 2t, y = 3 - 4t, z = 5 – 2t are…

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Q: Verify that the two planes are parallel. -x + 6y + 3z = 2 1 - x + 2y + z = 3 Find the normal vector,…

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Q: Find a nonzero vector parallel to the line of intersection of the two planes – (2x + 3y + z) = -2…

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Q: Find a vector of magnitude 2 parallel to the line of intersection of the planes x + 2y + z - 1 = 0…

A: Find a vector of magnitude 2 parallel to the line of intersection of the planes x + 2y + z - 1 = 0…

Q: Q1, Find Parame tric equations for the line through the Point (0,1, 2) that is U =i +2} + 3k and ū=…

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

Q: 3. Find a vector equation for the line through (2, 7, −3) that is orthogonal to the plane 3x + y −4z…

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Q: Show that the lines L1 : x = 2 – t, y = 2t, z = 1 +t and L2 : x = 1 + 2t, y = 3 – 4t, z = 5 – 2t are…

A: To show that the lines L1: x=2-t, y=2t, z=1+t and L2: x=1+2t, y=3-4t, z=5-2t are parallel and to…

Q: Find the domain of the vector tunction. (Entar your answer using interval notation.) r(t) = (V/25 -…

A: " Since you have asked multiple questions we will solve first question for you. If you need the…

Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

Q: Verify that the two planes are parallel. -x + 6y + 2z = 6 1 - x + + 3y + z = 7 2 Find the normal…

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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: orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

A: Here,        x = (3, 4)T       y = (-4, y2)T x and y is orthogonal if xTy = 0.

Q: Find the direction vector of the line of intersection of the planes x + 2y +z = O and x+y+1 = 0. %3D

A: Line of intersection of two planes

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

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Q: Find a vector v parallel to the intersection of the planes - (x + 3y + 4z) = 7 and 2y – 2x + 2z = 7.…

A: The direction vector of the line of intersection of two planes is parallel to the cross product of…

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

A:

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. If vector AB = i + 4j…

A: Given  AB=i+4j-2k and B is the point (5,1,3)

Q: • We have 2x 2y Vf(x, y, z) = i+ +1)j+6k. x² + y²- 1 x² + y? – 1 | Thus Vf(1,1,0) = 27 + 37 + 6K.

A: We have to show the steps for the above equation.

Q: -x + 6y + 2z = 6 1. -x + 3y + z = 7 2 Find the normal vector, n,, to -x + 6y + 2z = 6. n = 1 Find…

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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…

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Q: What is the magnitude of the vector v with initial point P = (-4, 3) and terminat piont Q = (2, -5)…

A: A detailed solution is given below

Q: Show that the point 1, - 2, 0 lies on both planes 3x-2y+z=7 and x-4y-2z=9. Hence, find the vector…

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Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y- 2z=3 is: *

A: Plan 1: 4x-y+z=2 Plan 2: 2x+y+2z=3

Q: If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the…

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Q: Verify that the two planes are parallel. -x + 6y + 3z = 2 -** + 2y + z = 3 Find the normal vector,…

A: We will use that if Ax+By+Cz=d is equation of plan than (A,B,C) is normal vector as well as…

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 that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

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Q: find the vector equation of a plane that contains the intersection line of x + y + z = 1 and x – y +…

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Q: Find the linear equation of the plane through the point (-3, 4, 3) and perpendicular to the line…

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Q: Find a position vector that is parallel to the line x = 2 + 4t, y = 5 - 8t, z = 9t.

A: The equation of the line is: x = 2 + 4t y = 5 - 8t z = 9t From the given equation of the line we…

Q: 2yz - 2yz2 + x at the point p = (1, -1, 1), find the unit vector that indicates the direction in…

A: Introduction:   The gradient of the temperature function at the point is the direction of the…

Q: Consider the line Siven by the Purumetric euvaton X=2434 Y=-1-+,2+ Q Find dinection vector of this…

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Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

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Q: Find the equation for the plane through the point Po= (9,2.5) and normal to the vector n= 31 + 10j +…

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Q: Show that the lines L1 : x = 4 – t, y = 2t, z = 5 +t and L2: x = 1+4t, y = 3 – 8t, z = 5 – 4t are…

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Q: The vector from the origin to point A is given as 4x-4y, and the unit vector directed fron the…

A: Please post the second question separately.

Q: Find the vector equation of the plane taking into account that 4x - y - z = 3

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Q: 1 Which vector is perpendicular to the plane -2x + 3y – 4z = 9? 1 1 2' 3 О 2, -3,4] 2 1 9 3? О 12,3,…

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Q: Find parametriequations for the line described below. The line through the point P(4, -3, 3)…

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Q: generate a parametrization of the line through P(2, -4, 7) parallel to v1 = 2i - j + 3k. Then…

A: We know that equation of line through (x1,y1,z1)  and parallel to ai+bj+ck is

Q: ) orthogonal to the vector y = (2)? You may want to go through the proof of When is the vector x =…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 3 1 - x + 3y + z = 4 -½-X 2 Find the normal…

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Q: Determine a vector equation of the line passing through (6, 0, 3) and parallel to the line of…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 4 -*+ 3y + z = 5 Find the normal vector, n,,…

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