2: (a) Find parametric equations for the line through the point (-6, 1,2) and the point of intersection line ***-- x+4 1 with plane x-3y + 2z 10. 5 -2

Q: Find parametric equations for the line passing through the points (10,3,1) and (8,6,-2) using the…

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Q: What is the parametric equation of line through the point (1,2, -1) and perpendicular to the plane…

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Q: Find parametric and symmetric equations for the line satisfying the given conditions. Through the…

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Q: fficients of x, y, and z in the given equation of the plane. ..... z= -7+ 9t. pe expressions using t…

A: Find parametric equation.

Q: The unit vector of the PQ (of point P(-3, 4, 1) and terminal point Q(-5, 2, 2)). - The angle between…

A: here we have

Q: 4. Find parametric equations of a line passing through (1, 2, 3) that is parallel to the plane…

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Q: 2) Find the parametric and symmetric equations for the line through (1, –1, 1) and parallel to the…

A: Solved below

Q: Find parametric equations for the line formed by the intersection of planes x + y - z = 29 and 3x -…

A: Consider the given:…

Q: Find parametric equations of the line through the point (8, 3, 4) that is parallel to the plane -2x…

A: First find vector normal to plane Write equation of line

Q: 3. Find a set of parametric equations for the line of the intersection of the planes 3x-3y-7z -4 and…

A:

Q: Find parametric equations of the line of intersection of the two planes. 9x + 8y - 9z = -3, -7x - 5y…

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Q: Q1: Find the parametric rquations of the line that passes through the point P(4,2,-3) and Q(-3,2,2).…

A: Here we have to find the parametric equation of the line that passes through the point P(4,2,-3) and…

Q: Find symmetric and parametric equations of the line through the two points (−3, 5, 2) and (1, −3,…

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Q: 4. Determine the parametric equation of the line that passes through (2, -1, 3) and is perpendicular…

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Q: Choose the parametric equations that represent the line segment that goes through the points (1,4,…

A: Given points x0,y0,z0=(1,4,-5) and x1y1,z1=(2,2,-1)

Q: 5. Find the parametric equations of the line that passes through the point (0, 1, 4)and is…

A: Given two vectors, u=2, -5, 1v=-3, 1, 4 Also, given the point, P=0,1,4 The cross product of u and v…

Q: . Determine the parametric equations of the curve of intersection of the ellipsoid 4x² + y² + 4z² =…

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Q: 2. Find the symmetric and parametric equations of the line containing the point A(1,2, 1) and x-2…

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Q: Find the parametric equation of the line through the points (−3, −2, 1) and(−1, −3, −1)

A: Given:

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

A: This is the problem from the vector algebra and 3D geometry.

Q: 5. Find the distance from the point (3, 0, 10) to the plane 2x+3y+ z = 2. 6. Write the parametric…

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

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

A: We need to find the vector equation of the line of intersection. In order to get it, we’ll need to…

Q: Find parametric equations of the line containing the .point (2, 3,-1) and normal to the plane x+…

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Q: Determine the parametric equations of the plane containing the point (1, -5, 9) and the line [x, y,…

A: I am going to calculate the parametric equations of the plane containing point (1,-5,9) and the line…

Q: Line 1: 1 - y = Z – 8 2 х — 3 4 Line 2: x=-2t y=2+2t z=6+2t 1.If the given lines intersect at a…

A: To find the given questions when two lines Line1 and Line2 are given :-

Q: 1. Find the point of intersection of the plane 3x+4y-2z=13 and the line given by parametric…

A: Given :  The equation of plane is 3x + 4y - 2z = 13. Parametric equation of the line is x = 1 +…

Q: Find a set of parametric equations and symmetric equations of the line ` con- taining the point P(1,…

A: Given Point is (1,-2,3) And Plan is : 2x-y+3z=6

Q: 4. Find the parametric equation of the line through (1, 0, -2) and parallel to the line (x-4) = 2…

A: The solution is given below in the next step:

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

A: we have to find parametric equations for the line that passes through the point  (5, 2) and is…

Q: 2. Find parametric equations of the line passing through (1, –3, 2) and perpendicular to the plane…

A: Parametric equations

Q: Find a set of parametric and symmetric equations of the line satisfying the following Passing…

A: According to the given information it is required to find a set of parametric equation of the line…

Q: 4- Find parametric and symmetric equations of the line passing through the points (1,- 1,2) and…

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Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4, 2)…

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Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 4x+2y…

A: Let F(x,y,z) define a surface that is differentiable at a point (x0,y0,z0), then the normal line to…

Q: 3. Find the parametric equation of the line passing through the point (-1,0, 3) and in the direction…

A: Equation of the line passing through the point (-1,0,3) in the direction N(7,0,-2) is   ( x+1)/ 7 =…

Q: Find parametric equations for the lines in The line through the point (3, -2, 1) parallel to the…

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Q: 6. Find the distance between the point (- 3, 2, 1) and the line with parametric equations x = 3 –…

A: Consider a point on the line (3-2t, 1-t, -3t) which is the foot of the perpendicular to the point…

Q: y+3x-6z=8

A: answer is in next step

Q: Find an equation ( in point - nomal form) of the plane containing the point (1.-3, 5) and the line…

A: Equation of a plane in point normal form is given as, A(x-a)+ B(y-b)+ C(z-c)=0 Where (A,B,C) is the…

Q: 7. Find the parametric equations of the line passing through A(1, -2, 6) and which is perpendicular…

A:

Q: Find a parametric equation for the line through the point (- 1, - 5, - 2) and perpendicular to the…

A: The parametric equation of the  line through the  points P0x0,y0,z0 and Plane a, b, c is x=x0+at…

Q: 5. Find the parametric equations of the line through A (-1, 2, 3) and B (2, 2, -3). Hence find where…

A: The set of parametric equations of a line passing through the points (x1,y1,z1) and (x2,y2,z2) are…

Q: 3. What is the parametric equation for the line through the point (1,2,3) parallel to the y - axis?

A:

Q: Find parametric equations for the line formed by the intersection of planes x+y-z=3 and 3x-y+3z=5.

A: First we find a point on the intersection of these planes with the plane z=0. And next find the…

Q: Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line…

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Q: Find the parametric and symmetric equation for the satisfying the given condition. 1. Through the…

A: Given : Equation of plane is y+3x-6z=8i.e. 3x+y-6z=8   To Find : Parametric and symmetric equation…

Q: 4. Find parametric equations of a line passing through (-1, 2, -2) that is parallel to the plane…

A: This question is based on 3-d geometry.

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