2 The equation of the plane passing through the origin and containing the vectors -1 and has equation 3 -4x + y + 3z 3x + 4z -x + 2y – 2z x + y + z 2т - у + 32

Q: 1 Suppose a line passes through the point (1, 1 and parallel to the 2' 3 plane x + y + z = 0. Then…

A: The direction vector of the normal to the plane is (1,1,1) Given that the line is parallel to the…

Q: Add the vectors u (0, 3) and i = (- 2, – 1) graphically. Your graph should include u, v and the…

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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: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

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Q: The scalar  equation of the plane passes through (-1, 3, -2), (-1, 2, -1) and (4, 1, -2) is:   a.…

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Q: Find the equation of the plane that is parallel to the vectors (1,0,2) and (0,1,1), passing through…

A: Sol Given                   Parallel to the vectors  &lt;0,1,2&gt; &amp;&lt; 0,1,1&gt;…

Q: The scalar equation of the plane passes through (-1, 3, -2), (-1, 2, -1) and (4, 1, -2) is: 2x + 5y…

A: Put the points one by one on the given planes and check satisfied or not

Q: . Find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q = (4, -2,1)…

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Q: 3. Two lines in the plane are perpendicular when the product of their slopes is -1. Apply this to…

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

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Q: Can three vectors in the xy plane, R^2, have u.v<0, v.w<0, w.u<0

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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: 13. Find an equation of the plane through the point (1,2,3) and perpendicular to the vector…

A: Given a point P( x, y, z) and a vector (a, b, c) which is perpendicular to the given plane

Q: The distance of a point in the 3-D system from the origin A. is defined by the absolute value of the…

A: Given :                To find the distance of a point in the 3-D system from the origin

Q: 1. Find equation of plane P containing point P,: (1,2,3) and the vectors v = (2,1,2) and w = (3,…

A: Solution:-Here we have to find the equation of the plane containing points P0:(1,2,3) and vectors…

Q: Find a vector parallel to the line of intersection of the planes 2x + y - 3z =13 and x + 3y + 5z =-8

A: Given, The equation of the planes  2x+y-3z=13 x+3y+5z=-8 We have to find a vector parallel to the…

Q: The plane contains the point (2, −1, 6) and is normal to the vector &lt;2, −1, 6&gt;.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

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: Find the equation of the plane that is parallel to the vectors 3,0,1 and 0,1,2​, passing through the…

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

A: The solution is given in the next step.

Q: The equation of plane through (3,-1,7) and perpendicular to the vector n(4,2,-5) is 4x + 2y5z-25 =…

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Q: 3. Give the parametric and symmetric equations of the line that passes through he point (4, –3, 5)…

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Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

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: 9. Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R…

A: Since there is multiple questions, we will solve the first question. Repost the question again and…

Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

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: 5- Investigate Interaction of Two Planes Plot the following and their normal vectors. x-y+z=-13 -3x…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Please reply as soon as posible Consider the vectors u = (1, -8,5) and v = (- 15.0, -3) The vector…

A: Given vectors are u = (1, -8,5) and v = (- 15.0, -3)

Q: Find the equation of the plane that is parallel to the vectors (2,0,2) and (0,1,3), passing through…

A: Solution: The objective is to find the equation of the plane that is parallel to the given vectors…

Q: 4

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Q: The volume of the parallel pipe formed by three vectors A, B, and C is 50 cubic units. if A(-2,6,3),…

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Q: Find an equation for the plane passing through the points Q(2, 1, –1), R(-1, 3, –1), S(3, 1, 0). 1.…

A: We know that equation of a plane is given by ax+by+cz+d=0 As it passes through (2,1,-1), we get…

Q: Find an equation of the plane that passes through the point (3, 2, 2) and is perpendicular to the…

A: equation of the plane passing through the points (3, 2, 2)               A(x-3)+B(y-2)+C(z-2) = 0…

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: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y2 + 2z2 + 4x – 4z = 0.

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Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

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Q: Find a vector n perpendicular to the plane determined by the three points A(1, -1,2), В(2, 0, — 1)…

A: Given three points ( position vectors) are; A( 1,-1, 2) , B( 2,0,-1) and C(0, 2,1)

Q: Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and…

A: The given problem is to find the vector equation of line that passes through the given two points.

Q: Find symmetric equations for the line that passes through the point (5, -2, 7) and is parallel to…

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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: 2) Find the vector from the origin to the center of the sphere 2x² + 2y² + 2z2 + 4x - 4z = 0.

A: The equation of the sphere is, 2x² + 2y² + 2z² + 4x - 4z = 0 So, x² + y² + z² + 2x - 2z = 0 So, (x²…

Q: find two distinct vectors on the line belonging to the intersection of the hyperplanes: Xi+ 2x2 - X3…

A: We need to find two distinct vectors on the line belonging to the intersection of the hyperplanes

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: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y² + 2z2 + 4x – 4z = 0. |

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Q: The equation of plane through (3,-1,7) and perpendicular to the vector (4,2,-5) is 4x + 2y5z-25 = 0.…

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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 an equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

A: Given An equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…