Consider the points P(1, −2, 3) and Q(2, 4, 0). (a) Represent the line ←→P Q by a vector-valued function. (b) Write an equation for the plane that contains the point P and is orthogonal to the line ←→P Q.

Q: Find a vector parallel to the line of intersection of the planes 2x + 3y – = =11 and 4x + 2y – 3= =…

A: Topic:- vector

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: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

A:

Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: We have, Equation of plane through P0 =(x0, y0, z0) with normal vector n = <a, b, c> Vector…

Q: Find an equation of the plane that passes through the point (1, 3, −7) and is perpendicular to the…

A: Direction ratio of the line n=j is (0,1,0)  Given that the line is perpendicular to the plane.  So…

Q: Find an equation of the plane that passes through the point (0, 0, 0) and is perpendicular to the…

A: The direction ratio of n = −3i + 2k is (-3,0,2) Given that that plane is perpendicular to n = −3i +…

Q: Find a vector parallel to the line of intersection of the planes 2x + 3y – z =11 and 4x + 2y – 3z =…

A: We need to find a vector parallel to the line of intersection of the planes 2x+3y-z=11 and 4x + 2y -…

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: Find a vector v parallel to the intersection of the planes - (2x + 4y + 3z) = 4 and 3x + y + z = 7.

A:

Q: | Find a vector equation for the line through the point (–9, –9, 3) parallel to the line 19 + 4t, y…

A:

Q: Find the vector equation of the intersection of the plane x+2y+3z=2 and x+3z=3  r=<  ,  , 0…

A:

Q: Find a nonzero vector parallel to the line of intersection of the two planes 3y+4z=−3 and 5x+y+2z=4

A:

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

A:

Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Find an equation of the plane that passes through the point P(-7,–5,5) and has the vector n = (-1,4,…

A: Given : Point P(-7,-5,5) and a normal vector n=<-1,4,2>   To Find : Equation of the plane that…

Q: (a) Prove that the planes 4.x – 2y + 6 = 0 and y – 4z – 13 = 0 intersect each other. (b) Find the…

A:

Q: Find a vector equation for the line through the point Pla,-1,0,3) that is orthogonl t the hyperplane…

A: Suppose a line passing through the fixed point with position vector a and parallel to vector b, then…

Q: Find an equation of the plane that passes through the point P(-4, -5, 4) and has the vector n =…

A: Plane passes through the point P-4, -5, 4 and has the vector n=-4, 9, 4 as a normal.

Q: Find the vector equation for the line of intersection of the planes 5x + 2y – 5z = 2 and 5x + 4z = 4…

A:

Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4 r=⟨ ,…

A:

Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4

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Q: Find a vector in component form that is perpendicular to the line 3x 4y = 6.

A: To find the vector in component form that is perpendicular to the given line.

Q: Find the vectorequationof the line of intersection of the planes  2x-3y–z=5 and x+y+2z=1

A:

Q: Find a vector v→parallel to the intersection of the planes 3x+y+2z=3 and       −(x+2y+4z)=7

A: Vector parallel to intersection of two planes is cross product of the normal vectors of the two…

Q: Determine the vector, parametric, and Cartesian (Scalar) equations for the line that passes through…

A: To find the equation of line that passes through the point A(4,-1) and is also perpendicular to line…

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P=(2,0,-4),…

A:

Q: Find a vector function that represents the plane that passes through thepoint p0 with position…

A: The plane passes through the point p0 whose position vector is r0→. The plane also passes through…

Q: Find a vector parametrization of the line through P = (3, -5, 7) in the direction v = (3, 0, 1)

A: Given:P=3,-5,7v=3,0,1

Q: Find a vector normal to the plane -2x - 3y = 12 - 4z.

A: Given  a vector -2x-y=12-4z. We need to find the vector normal to the plane.

Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

A:

Q: Find the orthogonal projection of the vector (2,4) about the line L parallel to the vector (-1,2)

A:

Q: A normal vector for the plane 4x −2y + 7z−11 = 0 is ______.

A: We have given equation of plane  4x-2y+7z-11=0 Then, we  can write this as…

Q: Find the value of c that will make the vector 2 lie in the span of 0 2 and

A:

Q: Show that direction vectors of the lines x-3y+ 1 L: and 2 -2 are orthogonal.

A: Direction vector of a line x-x1a=y-y1b=z-z1c   is   <a,b,c>  So, Write the direction vector of…

Q: Find an equation of the plane. The plane through the point (4, 0, -5) and perpendicular to the…

A:

Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: Find a vector v parallel to the intersection of the planes 3x + y + 2z = 3 and – (x + 2y + 4z) = 7.

A:

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: Find the vector equation of the plane taking into account that 4x - y - z = 3

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

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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…

A:

Q: A normal vector for the plane 4x – 2y + 7z – 11 = 0 is

A: Solution is given below:

Q: generate a parametrization of the line through P(2, -4, 7) parallel to v1 = 2i - j + 3k. Then…

A: We know that equation of line through (x1,y1,z1)  and parallel to ai+bj+ck is

Q: Find the vector equation for the line of intersection of the planes 4x + 2y + 2z -1 and 4x + z= -2…

A:

Q: Find a nonzero vector parallel to the line of intersection of the two planes 4y – 3x +3z = -2 and z…

A: Answer

Q: Find a nonzero vector parallel to the line of intersection of the two planes 5z – (3x+3y) : 2 and 2x…

A:

Q: Solve for the linear equation of the plane through the origin and perpendicular to the vector…

A: Topic:- geometry

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.