a) Find the scalar parametric form of the equation of the line which is parallel to the line of intersection of the planes x + 2y – z = 2 & 2x – y + 4z = 5 and passing through the point (2 b) Consider the vectors a = –4i – 7j , b = -i + 6k , c = i – 2j + k . Evaluate (b · a – |-3c|b .

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Q: 8. Find a vector parallel to the line of intersection of the two planes a – 2y + z = 1, 2x + y + z =…

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Q: What is the parametric equation for the line of intersection of the planes x + y - z = 2 and 3x - 4y…

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Q: a line is parallel to the vector 2i + 7j+ 8k and passes through the point P = (3,6, 6), then the…

A: Given query is to find the equation of the line.

Q: The equation of the plane passing through the point A(8, 10, 9) and orthogonal to the line x = 7+…

A: Given: Point A(8,10,9) Line x=7+8t , y=6+4t , z=5+9t

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Q: Find a vector parametric equation for the ellipse that lies on the plane 5y−3x+z=9 and is inside the…

A: Given that: 5y-3x+z=9 Let x=u cos v, y=u sin v So z=9+3x-5y  =9+3u cos v-5u sin v

Q: 5. Show that lines l and lz intersect, find the point of intersection, then find a parametric…

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Q: If a line is parallel to the vector 4i + 1j+ 4k and passes through the point P = (3,7,9), then the…

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Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find a.…

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Q: x = −1+5t y = 3-s-2t z= −2+s

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Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1:2x – y…

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Q: Find constants a, b, c such that  G( u, v) = ( u + av, bu + v, 2u - c) parametrizes the plane 3x - 4…

A: Given G( u, v) = ( u + av, bu + v, 2u - c) parametrizes the plane 3x - 4 y + z = 5.

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Q: (a) Consider the flat Fj C Rª described by the system of equations 3.x1 – x4 = 2 and Xi + x2 – x4 =…

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Q: (a) Find a vector parallel to the line of intersection of the planes 4x – y – 3z = 6 and -5x + 4y –…

A: SOLUTION-

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Q: If a line is parallel to the vector 6i + 7j+ 2k and passes through the point P= (5, 1,7), then the…

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Q: 12. a. Use vectors to show that the distance from P;(x1, Y1, Z1) to the plane Ax + By + Cz = D is…

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Q: If a line is parallel to the vector 3i + 2j + 1k and passes through the point P = (1,3, 8), then the…

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Q: Find a parametric form for the line through the point (0, –7, -9) and parallel to the vector 6i – 7j…

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Q: Find the point on the plane x - 2y + 3z = 12 that is closest to the point (0, 2, 2). (x, y, z) =

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Q: Find parametric equations for the lines in Exercises 1–4. 1. The line through (0, -7, 0)…

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Q: Find parametric equations for the lines in Exercises 1–4. 1. The line through the origin parallel to…

A: Hey, since there are multiple questions posted, we will answer the first two questions. If you want…

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Q: If a line is parallel to the vector 7i +9j + 9k and passes through the point P = (10,4, 1), then the…

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Q: 5. Show that lines lh and lz intersect, find the point of intersection, then find a parametric…

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Q: Question 10

A: We have to find equation of plane that is parallel to the plane 6x-5y+8z+18 =0 and  the pale passes…

Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1: 2x –…

A: 2)as per our guideline we have to write one question at a time kindly repost remaining questions

Q: If a line is parallel to the vector 7i + 5j+ 5k and passes through the point P=(4,3,5), then the…

A: To find the parametric equation of the line:Given line is parallel to the vector 7i+5j+5kSo, a=7,…

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 6z + 18 =…

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Q: (3) Write the equation of the plane which is perpendicular to the vector ñ² = (2₁-1₁-2) and touches…

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Q: If a line is parallel to the vector 7i + 9j+ 9k and passes through the point P= (2,9, 7), then the…

A: Given query is to find the equation of the line.

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