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

Q: Show that the vectors i - j, j - k, k - i are parallel to a plane.

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Q: 3. Find the Scalar eguation of the plane containing the line rt) =<!,2,-37+ -3,2, 17 and the point…

A: Given problem:- Find the scalar equation plane containing the line  r (t)= &lt;1,2,-3 &gt; + t &lt;…

Q: Find a vector equation for the line through the point (-3, –1,8) perpendicular to the vectors ū =…

A: vector equation can be find in the following way:-

Q: Find a vector equation with parameter t for the line through the points (–1, –7, –4) and (-9, 8, 2).

A: we know that vector equation of line which passes through pointsx1,y1,z1,x2,y2,z2 is given by…

Q: 2. Find the vector, parametric and cartesian equation of a plane that contains the points А(-1,0,…

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Q: Find the value of  x  so that the two vectors  (27,1,13)  and   (x,0,1)  are orthogonal

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Q: Express the vector v with initial point P and terminal point Q in component form. (Assume that each…

A: It is asked to represent the given vector with initial point P and terminal point Q in component…

Q: Do the vectors (1, 0, 0), (0, 1, 0), and (2, 3, 0) lie on the same plane? Briefly explain how you…

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Q: What is equation of the plane passing through the point A(-2,-1,-3) and paralleto the vectors a=3+2k…

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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: Determine the equations of the line (vector, parametric, Cartesian and general) that passes through…

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Q: 10

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Q: The line that passes through the point (4, –2, 0) and parallel to the vector (1, 2, –3) has…

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Q: Finally, verify that the vectors satisfy the Parallelogram Law |||² + ||||? 3. ī = (2, –1), w =…

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, –2), (2, 3, 4) is

A: Query- Find a vector orthogonal to the plane through the points -1,0,0,0,-2,-2,2,3,4. Answer- Let…

Q: The vector (3, -1, 2) is parallel to the plane 6x – 2y + 4z = 1. - %3D

A: Use formula to calculate equation of plane

Q: Find the equation of the plane through the point (-3,2, 0) and perpendicular to the vector (1,-2,5).

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

Q: Find a vector equation for the line through the point Pla,-1,0,3) that is orthogonl t the hyperplane…

A: Suppose a line passing through the fixed point with position vector a and parallel to vector b, then…

Q: The intersection of the two planes given by the vector equations ()- -2 =0 r. and -4 = 3 r. is

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Q: The plane contains the point (−2, 3, −1) and is normal to the vector 3i − 2j.

A: Given: point -2,3,-1   and vector 3i-2j

Q: Find the vector equation for the line of intersection of the planes 5x + 2y – 5z = 2 and 5x + 4z = 4…

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Q: Find the equation of the plane containing the point ( – 5, – 10, 9) and the two vectors and -

A: Given that , Plane containing the point -5,-10,9 So , a→=-5 i^-10 j^+9 k^ And vectors are ,…

Q: Let M be a plane that contains the point with coordinates (-2,-2,-1) and is orthogonal to the vector…

A: Let M be a plane that contains the point with coordinates -2, -2, -1 and is orthogonal to the vector…

Q: Give a vector parametric equation for the line that passes through the point (–2, 1, –2), parallel…

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Q: The plane that contains the points (-2,1,0), (1, 0, –1) and (0, –1, 1) is orthogonal to which…

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Q: For which positive value of r are the vectors (14r, 2, -1), (2, –3r², –10) orthogonal?

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Q: Find an equation of the plane passing through (0,-1,3) that is orthogonal to the planes 3x+4y-2z=0…

A: Let's find equation of the plane.

Q: Let vector AB = (2,3,1). If the coordinates of A are (2,1,5), what are the coordinates of the point…

A: Vector AB= B-A

Q: Consider the plane that goes through the point (4, 1, 3) and is orthogonal to vector (2, 3, 1).…

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, -2), (2,3, 4) is

A: A vector orthogonal to the plane through the points (-1,0,0) , (0,-2,-2) , (2,3,4) is

Q: Show that the vectors 3 do not span R° by giving a vector not in their span.

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Q: Find an equation of the plane through the point (29,-37,46) and with normal vector 14i+19j–17k.

A: we have to find an equation of the plane passing through the point (29,-37,46) and with normal…

Q: The terminal point of the vector v = 3i -j+ 5k with initial point (2, 5, -5) is Do not leave any…

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Q: Find the magnitude of the projection of ⟨-3,-2⟩ onto the vector ⟨1,-2⟩

A: I have appended the formula used in the solution part of the question

Q: 4 3 2 1 b. -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

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Q: Find the equation of the plane containing the points P = (−1, 3, 2),Q = (−5, 1, 1), and R = (6, 0,…

A: Given,             The plane containing the points P = (−1, 3, 2), Q = (−5, 1, 1) andR = (6, 0, −3).

Q: | Show that the vectors 2 do not span R³ by giving a vector not in their span.

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Q: The equation ax + by + cz = 0 represents a plane through the origin in R3. Show that the vector n2 =…

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Q: Find the equation of the plane that passes through the point (−2, 8, 4) and contains vectors ⃗a…

A: The equation of plane passing through the point x0, y0, z0 and contins vector a→ amd b→ is n1(x -…

Q: Find a vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

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Q: Find an equation of the plane that passes through the point P(-2, –4, 2) and has the vector (-5, 4,…

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, – 1, –2), (2, 3, 4) is

A: This could be solve using vector concept.

Q: Is the line passing through the point (3/2, 1) and slope −2 a hyperplane ? If yes, identify this…

A: Any line in 2D is a hyperplane.  ax+by=c, is a hyperplane (a,b) is called the normal vector  c is…

Q: Show that the vectors ( 1, 0,1) ; ( -1, 2,3) and (0, 1; -1) spans R³

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Q: Find the equation of the plane through the point (-3,2,0) and perpendicular to the vector (1, -2,5).…

A: Questions from vector calculus.

Q: Consider the plane that goes through the point (4, 1, 3) I to vector (2, 3, 1).

A: It is given that the plane is passing through the point (4,1,3) and orthogonal to the vector (2,3,1)…

Q: Find a vector equation for the line segment from (2, -1, 4) to (4, 6, 1)

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Q: Find a nonzero vector parallel to the line of intersection of the two planes 4x-2y+z=-1 and…

A: Answer

Q: Find the magnitude of the projection of (- 5, 6) onto the vector (– 1, 0)

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