Find the vector form of the equation of the line inR3 that passes through P = ( - 1, 0, 3) and is perpendicular to the plane with general equation x - 3y + 2z = 5.

Q: Find the vector form of the equation of the line inR3 that passes through P = ( -1, 0, 3) and is…

A: Equation of a line passes through  x1, y1, z1 having direction ratios a, b, c is, x-x1a=y-y1b=z-z1c

Q: Write down the position vectors of any two points on the line ˜ r · (3i − 4j) + 2 = 0 and hence find…

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Q: Find a vector normal to the plane with the given equation.9x − 4y − 11z = 2

A: Our Aim is to find a vector normal to the plane with the equation given below:-9x-4y-11x=2 -(i)

Q: 4. Write the vector equation for a line parallel to the line L: F = (1,-7)+t(2, -3), t € R…

A: Introduction: In three-dimensional geometry, a line can also be described through a vector equation,…

Q: Find the equation of the plane that contains the point (4, – 1, 3) and is perpendicular to the…

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Q: Find the new equation of the line y=x after applying the translation by the vector (2, -1)

A: New line will be shifted to 2 units right and 1 unit down.   Point on x axis (2,0) Point on y axis…

Q: Find the vector equation for the line of intersection of the planes 5x +y-3z= -3 and 5x + z = -1 r =…

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Q: The unit vector of the column on the plane 2x + 2z - 4y = 3 is the vector.

A: THE GIVEN QUESTION CAN SOLVED AS SHOWN IN STEP2.

Q: Given the points A(2,6,0) and B(3,5,6) determine the equation of a line vector in parametrix form

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Q: Find the vector equation for the line of intersection of the planes x + 4y + z = -5 and x + 4z = 0…

A: Here we have to find the vector equation for the line of intersection of the planes x+4y+z = -5 and…

Q: Find the scalar equation for the plane passing through the point P=(4, -5, 3) and containing the…

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Q: Find the vector equation of the line of intersection of the planes x+y+z=1 and x+2y+2z=1.

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Q: Find the equation of the plane passing through the point (3, 2, 2) perpendicular to the vector…

A: Given that the plane is perpendicular to the vector n=2i+3j-k. This means the direction ratio of the…

Q: Find the equation of the plane through the point with position vector 5i-2j+3k perpendicular to the…

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Q: Find the equation for the plane through the point Po = (3,4,3) and normal to the vector n=21 + 7j +…

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Q: Find the cartesian equation of the plane that is normal to the vector n = -3i – 4j+4k and includes…

A: n=-3i-4j+4k  and P(2,-7,5)

Q: equation

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Q: Find the equation of a line in vector form that is parallel to 3x−2y+z= 4, passes through the point…

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Q: Find the equation of a plane through the point (1, – 1, 6) and orthogonal to the line x(t) = 7 + 4t…

A: Required plane is orthogonal to the given line, say L: x(t)=7+4ty(t)=-3-4tz(t)=-1-6t also, the plane…

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

A: Given: (2,3,-6) Perpendicular to j vector

Q: Find an scalar equation of the plane containing the line x = 2 – 4t, y = 4 – 5t and z = 5+t and the…

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Q: Find a vector normal to the plane with the given equation. 2x + 8y + 9z = 3 n =

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Q: Find the equation for the plane through the point Po = (2,2,7) and normal to the vector n= 8i + 3j +…

A: Equation of plane passing through point P(x0,y0,z0) and normal to vector n=ai+bj+ck is given by:…

Q: c) Is the point (4,3, 3) on the line (L1) ? Why or why not ? d) Determine the vector equation of the…

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Q: B) find a vector that is parallel to the line whose equation is : 4-x 3-6z % = 3 – 3y = 5 9

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Q: 3. Write the scalar equation for a plane passing through (5,8,-1) and perpendicular to the line x =…

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Q: ) Write down the position vectors of any two points on the line T·(3i – 4j)+ 2 = 0 and hence find…

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Q: Find the scalar equation of the plane that contains the line x+1 -3=. and is parallel to x+2=+4_:+2…

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Q: In vector form, the equation of a line is given by r = (0, 1, 2) + t(2, 1,0), where t e R. T…

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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 a vector equation for the line through the point (2, 5, 8) perpendicular to the plane 2x + 5y +…

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

A: Hi there, At a time we can answer only one question. So, I have answered first one (#6).

Q: Find the vector equation for the line of intersection of the planes 5x + 4y + 5z = 1 and 5z + z = -4…

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

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Q: Find an equation of the plane that passes through the point (3, 2, 2) and is perpendicular to the…

A: equation of the plane passing through the points (3, 2, 2)               A(x-3)+B(y-2)+C(z-2) = 0…

Q: . The line (x-2z 3, y 22) intersects the plane (x+3y-:+4=0) at the point P, Find: (a) the…

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Q: Find the vector equation of the line that is perpindicular to the line q(t) = (1,2, 3) + s(2, –1, 1)…

A: Consider a point P(1+2s, 2-s, 3+s) on the vector equation of the line. The vector joining points P…

Q: a) The line y =- 5x + 9, in VECTOR form (R?).

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Q: Find the second and the third components of a vector n normal to the plane with the equation 7x +…

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Q: Find the vector equation of the line between the points (3, -1, 2) & (1, 4, -1), then graph the…

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Q: Show that A(x - x0) + B( y - y0) = 0 is an equation for the line in the xy-plane through the point…

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Q: Find the vector equation of the line of intersection of the planes x+y+z = 1 and x+2y + 2z = 1.

A: The equation of the line vector of the intersection of 2 planes can be calculated using the cross…

Q: Find the general form of the equation of the plane passing through the point and normal to the…

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Q: Find the value of d in the equation of the plane ax+by+cz+d=0 passing through the point P(3, 1, -2)…

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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 a vector equation of the line r through D4 and perpendicular to the line s through F4 and B1.…

A: Given,D4→ = 1i ^ + 2j^ + 3k^Equation of line passing through D4→ is:x-1a= y-2b=z-3cThe above line is…

Q: Find the equation of the plane passing through the point (2,−1, 3) and normal to the vector N = (2,…

A: we know that equation of plane which passes through point x1,y1,z1 and normal to vector a,b,c is…

Q: Find the vector equation of a line L going through the point P = (-5, -6) and parallel to the line…

A: The vector equation of line is

Q: Find a vector parallel to the line of intersection of the planes 4х + 2y - 33 %3D17 and 3x - 4y…

A: Vector parallel to the Inter section of two planes  a and b is cross product of a and b Let m is a…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.