Q2 What are the parametric equations for the line through the point (6,-3,1) that is orthogonal to the vectors V-i+3j+5k and L= 31 – 2j- 6k ?

Q: Find parametric equations for the line through (-2,0,4) parallel to V=2i +4j -2k .

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Q: B- Find the parametric equations for the line through point (1,0) and parallel to the function f(x,…

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

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Q: Q1, Find Paametric equations for the line through the Point (0,1, 2) that is U =i 12}+ 3k and ū= 3i…

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Q: a line is parallel to the vector 2i +7j+7k and passes through the point P = (7, 10, 3), then the…

A: Given query is to find indicated line.

Q: 33 and Complete the parametric equations for the line where the planes – 3x – 9y – 12z = - 11x + 2y…

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Q: A) Find the parametric equations for the line through the point P = (3.-5, 1) that is perpendicular…

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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: Find parametric equations for the line through (- 1,6, - 1) perpendicular to the plane 7x+ 5y + 5z =…

A: to find the parametric equations for line passing through (-1, 6, -1) and perpendicular to the…

Q: The planes 4x + 4y + 3z = -15 and y - 5x - 2z = 11 are not parallel, so they must %3D intersect…

A: Given: The planes 4x+4y+3z=-15 and y-5x-2z=11

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

A: Topic = Vector

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: Find parametric equations for the line through the origin parallel to the vector 3j + 9k. Let z =…

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Q: (a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5…

A: aLet the L1 be the line:x=1+t, y=1+6t,z=2tand L2 be the line:x=1+2s, y=5+15s, z=-2+6sThe direction…

Q: Find parametric equations of the line through (-1, –1, 6) that is parallel to 2i – 4j+k. x(t) = y(t)…

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

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Q: Find parametric equations for the line through (-2, 0, 4) parallel to v = 2i + 4j - 2k

A: we know that parametric equation of line which passes through point x0,y0,z0 and parallel to vector…

Q: 3. Write the scalar equation for a plane passing through (5,8,-1) and perpendicular to the line x =…

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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 parametric equations for the line through P0 = (3, −1, 1) perpendicular to the plane 3x + 5y −…

A: A line L in sace with direction vector d=d1,d2,d3 that asses throughthe point P=(x0,y0,z0) can be…

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

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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: 8) Find the parametric equation of the Line passes through p (2 -4,5) parallel 19to 3x+y-97 =5 and…

A: This question can be solved using the concepts: general equation of a line condition of  line and…

Q: Complete the parametric equations for the line where the planes 8x + 11y + 4z 13x + 2y + 3z = 5…

A: This question can be solved using the concept of lines and planes in three dimensional geometry.

Q: Find an equation of the plane in standard form (ax + by + cz = d) that passes through the point (4,…

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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: 4) a) Find the vector parametric equation of the line in R³ that is perpendicular to the plane 2x -…

A: Given plane is, 2x-3y+7z-4=0

Q: Find parametric equations of the line through (–3, 0, 3) that is parallel to 5i – 8j+ k. x(t) y(t)…

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Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

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

A: This is the answer of question no. 4.

Q: 30. Determine two sets of parametric equations for the line passing through the points P( 1,7, 1)…

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Q: Complete the parametric equations for the line where the planes 8x + 13y – z = 27 and 9x + 15y – 12z…

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Q: Find parametric equations of the line through (-2, –1, 3) that is parallel to 2i – 3j+k. x(t) = %3D…

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Q: Compute the parametric equations of the line in R3 determined by the intersection of the two planes:…

A: To obtain the parametric equations of the intersection line, use the following formulae. Let n1→…

Q: Find parametric equations for the line through (- 3,1,2) perpendicular to the plane 7x + 9y + 9z =…

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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: Complete the parametric equations for the line where the planes -4x + 2y – 14z = – 32 and -x – y –…

A: Use parametric equation of tangent line

Q: The planes 3x−4y+5z=−28 and 4x−2y+4z=−24 are not parallel, so they must intersect along a line that…

A:

Q: a) Prove that the lines with parametric equations: x = 1+ t, y = 1 + 6t, z = 2t and x = 1+ 2s, y = 5…

A: Given that: Line L1:  x=1+t, y=1+6t, z=2tLine L2:  x=1+2s, y=5+15s, z=-2+6s

Q: What is the parametric equations of the line through (2,2,2) parallel to the x- axis ? a) x = 2, y =…

A: 7) The Parametric equations of the line through (2, 2, 2)  parallel to x-axis is given…

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: The planes 5x+ 2y + 2z = 5 and 3x + 5y = -22 are not parallel, so they must intersect along a line…

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Q: Find a vector parallel to the line defined by the parametric equations x(t) - 3 – 9t y(t) 2 + 7t…

A: Need to find parallel vector and point on the line

Q: Find the parametric equations for the line of the intersection L of the two planes. 6x – 3y+ z = 5…

A: Parametric equations of the line is :  x(t) = x0 + a t  y(t) = y0 + b t  z(t) = z0 + c t  Here ( x0…

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

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.