The line I has equation r = 4i – 9j + 9k + 2(-2i + j- 2k). The point A has position vector 3i + 8j + 5k. (i) Show that the length of the perpendicular from A to l is 15. (ii) The line I lies in the plane with equation ax + by – 3z + 1 = 0, where a and b are constants. Find the values of a and b.

Q: Find parametric equations for the line in which the planes, x+2y-2z=5 and 5x-2y-z=0 intersects. Show…

A: Given, The equation of intersecting planes, x+2y-2z=5 and 5x-2y-z=0.   We have, x + 2y = 2z + 5 and…

Q: Find the equation for the plane through Po(-6,3,7) perpendicular to the following line. x= -6+t, y…

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Q: The plane equation that has 3.9 units distance to the plane 5x -2y + 3z= 4 is O a. 5.0x-4y+3z=56.1 O…

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Q: 9) Find an equation of the plane whose points are equidistance from the point (2,-1,1) to the point…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find the vector equation of the line that passes through (1,0,-3) and it's parallel to v=2i - 4j +…

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Q: 2. Find an equation of the plane parallel to the line

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Q: Find parametric equations of the line of intersection of the two planes. 9x + 8y - 9z = -3, -7x - 5y…

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Q: Find an equation for the plane parallel to – 2x + 9y – 2z 30 and containing the point (1, 4, 3)

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Q: The equation of plane through the origin and parallel to the plane 2x+ 5y – 4z = 8 is 2x + 5y – 4z =…

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Q: Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to the…

A: The symmetric equations of line are given by (x-xo)a = (y-yo)b = (z-zo)cwhere (x0, y0, z0) is a…

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: Find the linear equation of the plane through the point (1, 7, 6) and parallel to the plane x + 3y +…

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Q: Find equations of the line through the point (1, −1, 1) perpendicular to the line 3x = 2y = z and…

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Q: Find an equation of a plane through the point (1, -4, -3) which is orthogonal to the line x = -3 –…

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Q: The plane 6x + 8y + 60z = 700 intersects th of the highest and lowest points or coordinates

A: Given that the plane           6x+8y+60z=700  and the cone                            z2=x2+y2

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 an equation of the plane passing through the point perpendicular to the given vector or line.…

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Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

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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: The equation of plane through the origin and parallel to the plane 2x +5y-4z = 8 is 2x + 5y- 4z = 0.

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Q: Find the vector equation for the line of intersection of the planes 2x – 2y – 5z = 5 and 2a + 2z = 1

A: Given  equation of planes 2x-2y-5z=5 2x+2z=1

Q: Find an equation of the plane passing through the point perpendicular to the given vector or line.…

A: Given point is (0,4,0) and normal vector is -7i+5j.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: Equation of line passing through the point (x1,y1,z1) and is perpendicular to the plane (ai+bj+ck)…

Q: Find the distance from the point to the given plane. (1, -3, 4), 3x+2y+ 6z = 5

A: Distance from point to plane formula If Ax + By + Cz + D = 0 is a plane equation, then distance from…

Q: Find an equation of a plane through the point (0,−2,1) which is orthogonal to the line…

A: The equation of a plane passing through the given point is as follows.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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

A: we have to find the equation of line which is passes through the given point and perpendicular to…

Q: What is the equation of the plane through the point (4, -2, 3) and parallel to the plane 3x - 7z =…

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Q: Find the general equation of the plane perpendicular to the line z – 2 y + 4 1- x = 3 and is 3…

A: We have to find the equation of plane.

Q: Find the linear equation of the plane through the point (-3, 4, 3) and perpendicular to the line…

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Q: 1. Find an equation for the plane through Po (0,2,-1) perpendicular to n = 3i - 2 j- k ?

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

Q: Find the general equation of the plane perpendicular to the line Z – 2 y+ 4 1- x = 3 and is 3…

A: This is a problem of vector algebra and geometry.

Q: Find parametric equations for the line in which the planes, X+2y-2z=5 and 5x-2y-z=0 intersects. Show…

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Q: Find the general equation of the plane which goes through the point (3,1,0) and is perpendicular to…

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

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: The planes 3x + 6z line. = 1 and 2x + 2y - z = 3 intersect in a a) Show that the planes are…

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Q: Find the equation of the plane that passes through the point (1,0,-2) and contains the line with…

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Q: The plane containing the point (-4,1,3) and parallel to the plane 4x + 7y – 3z = 2 has equation Ar +…

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Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

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Q: Find the equation of a plane that is perpendicular to the vector 2i+4j−3k and passing through the…

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Q: Q2 / A man moved from the point (2, -2, 1) to the point (8, 3, 4). Express the displacement moved by…

A: The given point is                    P1 (2, -2, 1)  and  P2 (8, 3, 4) To find displacement in terms…

Q: Find an equation of the plane that is parallel to the plane x + 2y – 7z + 15 = 0 and contains the…

A: A detailed solution is given below.

Q: A line has parametric equations x = 2 +3t, y = 1 + 2t, z = -6 - t, fort that belongsto the family of…

A: given parametric equation of line  is x=2+3ty=1+2tz=-6-t

Q: Find the equation of a plane that is perpendicular to the vector 4i+4j−3k and passing through the…

A: On solving this we will get

Q: Find an equation of a plane through the point (-2, 1, 5) which is orthogonal to the line 2= -3- 3t,…

A: The director vector of the line is (-3, -4, -3). Given that the plane is orthogonal to the line. So…