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

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

A: Explanation of the answer is as follows

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 an equation of the plane. The plane through the point (1, 7, 2) and with normal vector 4i + j –…

A: Given:   Point : ( 1 , 7 , 2)  Normal vector : 4i + j - k

Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x= 2+3t y…

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Q: Parametrize the line that passes through the point (1,2,3) parallel to the vector v = -3i + 7k.

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Q: Find the vector equation of the intersection of the plane x+2y+3z=2 and x+3z=3  r=<  ,  , 0…

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Q: What is the vector parametric equation L(t) for the line through the points (5,-5,0) and (0,-3,3)?

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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: O Find the parametric equation of the line through the point (-3,1,6) parallel to the vector V 2i +…

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given vectors area. u=2,0,2w=-2,-1,0a=0,0,0 Find the vector equation of the line perpendicular to u…

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

A: Vector equation of the line passing through point (a,b,c) and perpendicular to vectors u→ and v→ is…

Q: Find an equation of the plane that passes through the point P(-7,–5,5) and has the vector n = (-1,4,…

A: Given : Point P(-7,-5,5) and a normal vector n=<-1,4,2>   To Find : Equation of the plane that…

Q: Find the equation of the plane through the point with position vector 5i-2j+3k perpendicular to the…

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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: Parametrize the line that passes through the point (1, 2, 3) parallel to the vector v =-3i + 7k.

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

Q: 1 - Find a vector equation and parametric equations for the line segment connecting P(a, b, c) and…

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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 a vector equation for the line segment connecting the points P = (-9,–6, 8) and Q = (-15,…

A: We have to find a vector equation for the line segment connecting the points P=-9,-6,8 and…

Q: Find a unit vector perpendicular to plane PQR determined by the points P(-3, 3, -4), Q(4, -1, - 23),…

A: Given query is to find unit vector perpendicular to PQR.

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: Find an equation of the plane. The plane through the point (6, 1, 5) and with normal vector 5i + j -…

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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: 3. Find the equation of the line that goes through the point (1, 3, 2) and is parallel to the line…

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

Q: Determine the vector, parametric and cartesian (scalar) equations for the line that passes through…

A: First, we will find the cartesian equation of the line L through the points M(-2,0) and N(3,-3).…

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: Find an equation of the plane that contains the point (-1, 2, 3) and is perpendicular to the line…

A: The plane is perpendicular to the line, then the direction vector of the line is normal to the…

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

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Q: Find an equation of the plane. The plane through the point (4, 0, -5) and perpendicular to the…

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

A: Equation of the line passing through a given point a,b,c and in a given direction l i+m j+n k is…

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: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (2, –5) + t(1,…

A: Parametric equation of the line, <x,y,z>=<a,b,c>+t<p,q,r> , t is a scalar is given…

Q: Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).

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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…

A: We have to write a parametric equation of the line  which is passing through the point (-1, -1)…

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

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: u = < 0,2,2>  w = < 2,-2,0>  U× W is perpendicular to both u and w

Q: Give a vector parametric equation for the line through the point (1,−4,1) that is parallel to the…

A: We have to find the vector parametric equation for the line through the point (1,-4,1) that is…

Q: Find parametric equations for the line whose vector equation is (a) (x, y) = (3, –5) + t(1, –2) X =…

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

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

Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(1, −1,…

A: Find a  vector equation and parametric equation for the line joining P and QP (1,-1,5) and Q (5,2,1)

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: Find parametric equations for the line whose vector equation is given. (а) («, у) %3D (3, —3) + t(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: Find a vector equation and parametric equations in t for the line through the point and parallel to…

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

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