3. Determine vector and parametric equations for the plane through the point (1, -2, 3) and parallel to the xy-plane. Show your work. Тext

Q: Find the vector parametric equations for the line. in the direction of the vector – i+ 5j-3 k and…

A: equation of line in vector parametric form

Q: Give a vector parametric equation for the line through the point (3, 1) that is perpendicular to the…

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Q: Find the standard vector parametric equation of the plane curve given by 24x + 6y + 96 x- 48 y +96 =…

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Q: Find parametric equations for the line whose vector equation is given (a) (x, y) = (3, –5) + t(1,…

A: A)x, y =3, -5 + t 1, -2x, y =3, -5 + t, -2tx, y =3+t, -5-2t Parametric equations of the line:x= 3 +…

Q: Find the angle between the two planes 6x − 3y + z = 5,  −x + y + 5z = 5 and find a set of parametric…

A: We have given the equation of planes; 6x − 3y + z = 5 −x + y + 5z = 5 Hence the normal vectors of…

Q: Find an equation of the plane. the plane through the point (5, 6, 5) and with normal vector 6i + 8j…

A: As we know that the equation of the plane which is passing through a point Px0,y0,z0  and normal…

Q: Find the parametric equations for the lines. Where, the line through the point P (3, -4, -1)…

A: Topic = Vector

Q: Ps Fnd Parametric equations for the 3. lines through (2,3,0) Perpendliculerr to the Vector uiitzj+3k…

A: First take cross product ie normal vector And then use formula

Q: Find a parametric equation for the line through the point(1,9,3) and perpendicular to the plwne…

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Q: 8. Find a parametric representation of the line through the point P(1,0,4) and perpendicular to the…

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Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x-2y+z = 4.

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Q: Determine the vector equation of the plane 5x – 2y + 3z + 24 = 0. Verify mathematically that your…

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Q: Find the parametric equation for the line in R' that passes through the point (1, –2, 3) and that is…

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Q: Determine the general equation of the plane Ω passing through the point P(1,−4,−5) and parallel to…

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Q: Give a vector parametric equation for the line that passes through the point (3, 5, –5), parallel to…

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Q: Find the angle between the two planes 3x + 2y − z = 7,  x − 4y + 2z = 0 and find a set of parametric…

A: Known fact: The angle between two planes a1x+b1y+c1z+d1=0  and a2x+b2y+c2z+d2=0 is given by…

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A: we have to find the normal and general forms of the equation of the plane that contains the point…

Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

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Q: Find the parametric equations of the line through the point P(1, 2, 4) and parallel to the vector .

A: use the parametric form  of line .

Q: Find parametric equations for the line whose vector equation is given. (а) (т, у) 3 (6, —5) + t(1,…

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Q: Find the general equation of the plane containing the point (2,-1,4) and normal to the line 2 I+3…

A: The equation of the line passing through the points x1,y1,z1 with direction ratios a, b and c is…

Q: 8. Determine a vector equation for the plane with Cartesian equation: 2x -y + 3z-24 = 0

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Q: Find the parametric equations for the line through the point of intersection of the lines L1:x = 2 +…

A: In line L1 and L2  't' is used as parameter but don't confuse with it. Different different line we…

Q: Find a parametric equation for the line through the point (6,5, - 3) and perpendicular to the plane…

A: Given plane is, 7x+4y+4z=15 Since, the line is perpendicular to the plane then the normal vector…

Q: The side of S is given by x² + y = 16, and its height is 4. (a) Give a parametric equation, r(t) for…

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Q: How do you use a point on a plane and a vector normal to the plane to find the equation of the…

A: A vector normal to the plane will be perpendicular to all the vectors lying in the plane. We know…

Q: The planes 5x+y+z=−6 and 3y+5z=22 are not parallel, so they must intersect along a line that is…

A: Given planes are 5x+y+z=-6 and 3y+5z=22 find the vector parametric equation

Q: Find the parametric equations for the line through the point (5, 2, 9) and perpendicular to the…

A: The parametric equation of a line passing through the point and has a direction cosines <a , b…

Q: Find a parametric equation for the line through the point (2,3, – 1) and perpendicular to the plane…

A: Given that The point on the line (2,3,-1) and perpendicular to the plane 8x+3y+3z=5 A vector…

Q: Find the general equation of the plane through the point (1, 1, 1) that is perpendicular to the line…

A: We know that equation of plane which passes through pointx1,y1,z1 and perpendicular to linex=x2+at,…

Q: Find the parametric equation of the line of intersection of two planes correctly: P1:x+3y+5z=0 and…

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Q: Find the set of symmetric and parametric equations of the line passing through the point P(3, 4, 1)…

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Q: Provide the point-normal form equation of the plane containing (1, -1, 4) and line with parametric…

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Q: Find the parametric equations for the line through the point P = (-1, 4, -4) that is perpendicular…

A: Normal vector perpendicular to the plane 2x−4y−2z=1 is: (2, -4, -2) The line passes through P = (-1,…

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+y-2z = 3.

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Q: Give a vector parametric equation for the line through the point (4, 0, -5) that is parallel to the…

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Q: Find the parametric equations for the line through the point P=(-5,4,-1) that is perpendicular to…

A: The direction vector for this line is v=2,-1,-5 and it must pass through the point -5,4,-1. Thus we…

Q: Write the parametric and scalar equations of the plane given its vector equation [x, y, z] = [4, 3,…

A: Parametric equation is simple: x = 4 + 2s + 6t y = 3 + s + 6t z = -5 + 4s - 3t

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

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Q: Find parametric equations for the line whose vector equation is given. (а) («, у) %3D (3, —3) + t(1,…

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Q: Q2 What are the parametric equations for the line through the point (6,-3,1) that is orthogonal to…

A: We have to find the equation of parametric line

Q: The line L is parallel to the plane x+y+z=2 and is perpendicular to the vector (-1,1,–2). If the…

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Q: Derive the parametric equations of the line of intersection of the two planes: II : x – 2y + z =1…

A: Given: P1:   x−2y+z=1P2:   2x−2y−4z=4