let L1 and L2 be the lines whose parametric equations are x-3 z-1 L1 == y - 4 = 1 =yー4= -= y – 2 4 х — 1 у-3 L2 z - 4 4 2 8 a- Determine whether the lines are parallel ,skew or intersecting b- The distance between the Li and L2 .

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

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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: Find parametric equations for the line described below. The line through the point P(-1, -1, 5)…

A: Question 17 In general, we know that the equation of the line passing through the point (x1, y1, z1)…

Q: Find a set of parametric equation of the line through the point (1, 0, 1) parallel to the line x = 3…

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Q: Find parametric equations for the line going through (5, 4, 6) and is perpendicular to the plane x −…

A: Here, By substituting the values of r0 and v in vector equation,

Q: Find the parametric equation of the lines passing through (4, -2, 5) and (-3, 0, 6)?

A: Consider the two given points (4,-2,5) and (-3,0,6). The objective of the problem is to find the…

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: Find parametric equations for the lines in The line through (2, 4, 5) perpendicular to the plane 3x…

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Q: Find the parametric equations for the line in which the planes -4x +y+3= = 5 and 2x+y+ = 3…

A: Given that:-4x+y+3z=5    .............(1)2x+y+z=3          ..............(2)

Q: Find parametric equations for the line segment joining the points (6, 2) and (9, 10). x=t, y 2+8t,…

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Q: Find parametric equations for the line pass- ing through the point P(2, –1, 4) and parallel to the…

A: Given, The line is passing through the point  P 2, -1, 4  and parallel to the vector 1, 4, -2. We…

Q: Find the set of parametric equations of the line through the point (1, 6, 3) that is parallel to the…

A: The direction ratio of the line x=6+5t, y=6+2t, z=4+2t is (5,2,2). Parallel lines have the same…

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

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Q: Suppose a line is given parametrically by the equation L (t) = (2 -t.t-1, -t-2). Then the vector and…

A: Given:    Parametric equation L(t) = (2 - t , t - 1, - t - 2)    The line containing the point (x0,…

Q: Give the general equation of a plane which has point (1,2, -1) together with line with symmetric…

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Q: Find the distance between the skew lines with parametric equations x = 3 + t, y = 1 + 6t, z = 2t,…

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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: The scalar equation of the line perpendicular to (x, y) = (5, 2) +r(1, -3) through the point (2, -2)…

A: The scalar equation of a line is of the form Ax+By+C=0

Q: Find the parametric equation for the line through the point (2,-3,1) and parallel to the vector…

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Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it using…

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

A: We have to find the equation of the line passing through the point (1,2,-1) and normal to the plane…

Q: Find parametric equations for the line described below. The line through the point P(7, -4, 0) and…

A: NOTE: Refresh your page if you can't see any equations. . the given plane is  the normal vector is…

Q: Find parametric equations for the lines in The line through (0, -7, 0) perpendicular to the plane x…

A: we know that equation of line in parametric form which passes through pointx1,y1,z1 and…

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

A: The equation of the plane is given by 2x-y-5z=0. The directional cosine of the normal to this plane…

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

A: We have to find the parametric  equation of the line.

Q: Find parametric equations for the line in which the planes x + 2y + z = 1 and x - y + 2z =-8…

A: x + 2y + z = 1 and x - y + 2z =-8 are the two planes.Let z=t So, the equations become:

Q: Find parametric equations of the line that satisfies the stated conditions. The line through (- 5,…

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Q: 1. Find the vector and parametric equations for a line passing through (7,-4, 2) and parallel to the…

A: We have to find the vector and parametric equation of the line

Q: Find the symmetric and parametric equation of the line that is the intersection between the planes…

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

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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: Let L1 and L2 be the lines whose parametric equations are L1 :x= -63 +9t,y = 10 – 21, z = 45 – 6t L2…

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Q: Let Lj and L2 be the lines whose parametric equations are Li :x = -10+21, y = 25 – 81, z = 17 – 6t…

A: L1 : x=-10+2t,  y=25-8t,  z=17-6tL2 : x=52-6t,  y=-43+4t,  z=20-3t

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

A: Vector equation of line which passes through point r0 and perpendicular to line a+bt,c+dt is given…

Q: Consider line L of symmetric equations (-x = y+ 2, z = 3), a) Find point P that belongs to the line…

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Q: Find the parametric equation for line l that is parallel to line m with equation: x = 1 + 4t; y = -…

A: Two lines are said to be parallel if their direction ratios are proportional. We will use this fact…

Q: Write the parametric equations of the line through the point P (-6, 4, 3), that is perpendicular to…

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Q: Find parametric equations for lines passing through point Pand parallel to vector n: (а) Р(3, — 1,…

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

A: The parallel line through the point has the vector equation L = < 8,3,4 > + t < a, b, c…

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 described below. The line through the point P(1, 1, -2)…

A: Use equation of parametric line and put value

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: Find parametric equations of the line through (-3,1,1) that is parallel to 2i – 5j+k. -

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Q: Suppose a line is given parametrically by the equation L(t)=(1-t, t-4, 1-t) then the vector u and…

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Q: The angle and the parametric equations for the intersect line between planes x + y = 1, and 2x + y–…

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Q: Find the parametric equation of the line through (1, 0, -2) and parallel to the line % (x – 4) = ½…

A: according to our guideline we are supposed to answer only the first question if you want any…

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