Find parametric and symmetric equations of the line (i) through the points A(1, −2, 3) and B(2, 0, −2); (ii) through the point A(1, −2, 3) and perpendicular to u = <2, 0, 3> and v = <3, 2, −1>.

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

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Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-4, 0,…

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Q: Write vector and parametric equations of the plane a) parallel to the lines [x, y, z]= [1, - 2, 7]+…

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Q: Give the parametric and symmetric equations of the line that passes through the point (4, -3,5) and…

A: Using the dot product equal to zero for perpendicular to the vectors.

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

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Q: 6. Write vector and parametric equations of the plane. a) parallel to the xz-plane and through the…

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Q: Find the equation of the plane through the point (-3,2, 0) and perpendicular to the vector (1,-2,5).

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

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: Show clear and detailed solutions Provide the parametric and symmetric equations of the line that…

A: Let the direction ratio of required line is  l , m and n

Q: 3. Does the parametric equation r = (2,-5,2) + s(1,4,2)+(-2,-3,1), s,/€ R, and the vector equation…

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Q: Determine vector and parametric equations for the line through the point (2, 1) and parallel to the…

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Q: Determine the parametric and symmetric equation of line passing through the points (1, –3,2), (5,…

A: To find the parametric and symmetric equation of line passing through the points (1,-3,2) ,(5,-2,8)…

Q: Find parametric equation of the line passing through point (4,2) and parallel to vector 7 = -i+5j.

A: Given: A line passes through the point (4, 2). The line is parallel to the direction vector…

Q: Find the distance between the point (0, 2, 1) and the plane 2x − 6y + 3z = 6

A: Distance between the point x1,y1,z1 and the plane ax+vby+cz+d=0is given by-d=ax1+by1+cz1+da2+b2+c2

Q: 3. Give the parametric and symmetric equations of the line that passes through the point (4,-3,5)…

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Q: Find the parametric equations of the plane that contains the point (3,-2,0) and is parallel to the…

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Q: How do you find the parametric and symmetric equation of the line passing through the point (3, 2,…

A: We have to find the parametric and symmetric form of the line perpendicular to the given plane at a…

Q: Equation of the plane passing through the point (4, –2, –1) and parallel to yz-plane is

A: To find the equation of the plane passing through the point 4, -2, -1 and parallel to yz-plane.

Q: Find parametric equations of the line perpendicular to the yz-plane passing through the point (-3,…

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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: 3. Give the parametric and symmetric equations of the line that passes through he point (4, –3, 5)…

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Q: 3) Find a vector equation and parametric equations for the line segment that joins (-2, 4, 0) to…

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Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-9,0,…

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Q: Find the distance from the point (2,-3,5) to the plane passes through the points (1,0,-3), (3,4,-6)…

A: (b) Given point P2,−3,5 and a plane passes through the points 1,0,−3, 3,4,−6 We have to find the…

Q: Find a parametric equation and symmetric equation of the line that pases through the point (2, -1,3)…

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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: Determine the general equation of plane I passing through the point (-4, 3,-1) and parallel to the…

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Q: Find the parametric equations of the line containing the point (-2,1,2) and parallel to the vector…

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

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

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Q: Find parametric (or vector) and symmetric equations of the line which pass through the points P,…

A: P11, 4, 6 &amp; P22, -1, 3. Vector equation of a line passing through two points with position…

Q: Provide the parametric and symmetric equations of the line that passes through the point (4, -3, 5)…

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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 parametric equations for the line described below. The line through the point P(2, 3, 3)…

A: To find the parameter equation of the line passing through point P(2, 3, 3) parallel to the vector…

Q: Find the point of intersection of the line through (1, -3, 1) and (3, -10, 5), and the plane given…

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Q: (1 point) Find the point at which the line (-2, 1, –5) + t(-1,–1, –2) intersects the plane 4x – 2y +…

A: To findcthe point at which the line (-2,1,-5)+t(-1,-1,2) intersects the plane 4x-2y+2z=-68

Q: 2. Obtain an equation for a plane a that includes straight line(2--5) and 1: point(-2,1,1)

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Q: Find symmetric equations for the line through the point (1, -2, -4) which is orthogonal to the plane…

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Q: Find an equation of the plane. The plane through the point  (5, −5, −2)  and parallel to the plane…

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Q: Give the parametric and symmetric equations of the line that passes through the point (4,-3, 5) and…

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Q: Find the equation of the plane through the point (-3,2,0) and perpendicular to the vector (1, -2,5).…

A: Questions from vector calculus.

Q: Equation of the plane passing through the point (3, –2, 5) and parallel to yz-plane is

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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: 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: Find an equation of the plane. The plane through the point (7, –2, –8) and parallel to the plane 6x…

A: We will solve the following.

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: Find parametric equations of the line that satisfies the stated conditions. The line through (-8, 0,…

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