Find both the vector equation and the parametric equations of the line through (0,0,4) in the direction of the vectorv = (3, - 6,0), where t= 0 corresponds to the given point. The vector equation is (x,y,z) = (OO) +

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Q: Find both the vector equation and the parametric equations of the line through (4,3,6) that is…

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Q: Find the distance from the origin to the plane through the point (-6,3, -2) and having 5i - 3j° + 4k…

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

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A: We will solve the problem.

Q: Find an equation of the plane. The plane through the point (2, 9, 6) and with normal vector 7i + j –…

A: Find an equation of the plane

Q: Find an equation of the plane. The plane through the point (8, 7, 1) and with normal vector 7i + j -…

A: The equation of the plane is given as:

Q: Find a vector equation with parameter t for the line through the points (-1, –7, –4) and (-6, 8, 2).…

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Q: Find the terminal point of a vector of magnitude 5 that is parallel to the vector 1, 2, 3 and whose…

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

A: Question is solved.

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A: Use the direct formula for equation of plane passes through a point and with given normal vector.

Q: 3) Write down the equation of line in a vector parametric form, scalar parametric form and standard…

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Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: we have to represent the line segment from P to Q by a vector valued function and by a set of…

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) and (5,2,4),…

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

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Q: 2. Convert the vector A=10ax in the Cartesian Coordinates into a vector expressed in the Cylindrical…

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Q: Give a vector parametric equation for the line through the point (4, 2) that is perpendicular to the…

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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: Find a vector equation and a parametric equation for the line that passes through the point (5, 1,…

A: We have to solve given problem:

Q: Write the scalar equation of the plane with normal vector = [1, 2, 1)] and passing through the point…

A: here normal vector is  and the given point is

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: 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 an equation of the plane that passes through the point Po(0,2, – 2) with a normal vector n =…

A: Find an equation of the plane that passes through the point p0 (0,2,-2)with a normal vector…

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 the vector parametric equations for the line. in the direction of the vector 4 i – 3j- 3k and…

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Q: 4. Determine a vector equation for the plane that is parallel to the xy -plane and passes through…

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Q: Find an equation of the plane. The plane through the point (9, 3, 4) and with normal vector 8i + j…

A: To find- equation of  the plane.

Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

A: The equation of plane with normal vector (a,b,c) passing through the point p0 =(x0 ,y0 ,z0 ) is…

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

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

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Q: Find an equation of the plane. The plane through the point (4, 8, 6) and with normal vector 7i + j -…

A: Given, The plane passing through the point (4,8,6) with the normal vector 7i+j-k We know that, The…

Q: snip1

A: The given point is, P=1,2,-1 which is parallel to the vector d=5-13. The objective is to find the…

Q: Find an equation of the plane that passes through the point P(-3, -2, 3) and has the vector n = (-7,…

A: Find an equation of the plane that passes through the point P(-3, -2, 3) and has the vector n = (-7,…

Q: Write the vector A = 2z1-xi + yk in cylindrical coordinates.

A: *concept:- cylindrical co-ordinate = (x, y, z).

Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

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Q: Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.

A: Explanation of the solution is given below...

Q: Find a vector equation and parametric equations for the line segment that joins P to Q, given P(0,…

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Q: Write the scalar equation of the plane with normal vector * - [3, 4, – 1] and passing through the…

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Q: Write the equation of the plane with normal vector n = (1, 3, 4) passing through the point (3, -1,…

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Q: Find the distance of the point (2, 6, –4) from the line r(t) = (-1 + 31, –1+41, 5 – 2t). Give a…

A: Consider the given point as, 2,6,-4  And the line -1+3t,-1+4t,5-2t

Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

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Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: Given information: The points are P(0, 0, 0), Q(5, 2, 2). Calculation: Find the vector valued…