3. Let A, B and C be the points with position vectors 2 a = -- (:)). - (1) · - - () 1 b= 5 C = 3 respectively, and let II be the plane which contains the points A, B and C. (i) Find a Cartesian equation for the plane II. (ii) Find the distance between the plane II and the point with coordinates (0, 1, 0) (i.e. the point whose position vector is j). (iii) What is the position vector of the point on II which is closest to Q?

Q: What is the distance from the point P=(2, -1, 4) to the plane 3x+5y-2z =20

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Q: Given the points A(7, -2, -9 ) and B( 7, −2, 2 ). Question 3 a) [:] Write parametric and symmetric…

A: We have to find the equation of line and intersection of line and plane.

Q: 7. A line has equation /:*-=-= 1:*=1==32₁2=3 x-1 y-2 -,Z=3 z a) Write the parametric equation for…

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Q: 5. (a) Given A = a,5-ay2 + a₂, find the expression of a unit vector of B such that B/A and BL A, if…

A: Solution 5(a): Given that A→=5ax-2ay+az and  B→∥A→ if B→ lies in the xy-plane. So, B→=5bx-2by. Unit…

Q: 8. Find the parametric equations for the plane that passes through the points: P (2, -2, 3), Q (0,…

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Q: Let I be the line with parametric equations x = -9-2t y=-10+3t z=4+t Find the vector equation for a…

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Q: 3. (a) ) The points A(5, -10) and B(-7,6) are the ends of a diameter of circle C, Determine the…

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Q: Find a set of parametric equations of a line passing through the point (3,2,-1), parallel to the xz-…

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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: Determine parametric equations of the line of intersection of the planes x+2y+3z=4 and -2x+z=0. Then…

A: Let us consider two planes ax+by+cz+d=0 and a'x+b'y+c'z+d'=0  Intersection of two planes is line…

Q: a) Find an equation of the sphere with center (1.-3,-5) and tangent to xz-plane.

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Q: Given a plane 7, is orthogonal to line x-3=y =-z and goes through a point (-2, 4,1). Find the…

A: Equation of a plane passing through the point x1,y1,z1 and normal to the vector a,b,c is…

Q: 9. (a) What are the two properties that determine a line in space? Give parametric equations for a…

A: To find the parametric equations for the line through the given points and to mention the properties…

Q: 1. A line L passes throught point (2,-1,5) that is parallel to line given by l(t) = (t, −1+t, 2).…

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Q: A plane contains the point B(-3, 2, -4) and the line with parametric equations x= 1 + 2?, y = −t, z=…

A: Explanation of the answer is as follows

Q: 3. A plane contains A(1, -3, 2), B(-2, 4, 2) and C(3, 2, 1). (a) Determine the vector equation of…

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Q: Find a parametric equation of a line that passes through the point (1,3,-4) and is perpendicular to…

A: To find a parametric equation of a line that passes through the point 1, 3, -4 and is perpendicular…

Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is

A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.

Q: the

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