Find the point A (a, a, 0) on the line y = x in the xy-plane, such that the vector AB is perpendicular to the line OA. Here, O is the origin and B is the point (2, 4, -3)

Q: Find a unit norm vector that is orthogonal to both the vector (1,2, –1) and the line of intersection…

A:

Q: Find the coordinates of a point P on the line and a vector v parallel to the x - 7 y + 9 = z + 4…

A:

Q: Find a unit vector normal to the plane containing v=2i+3j-k and . w = -2i - 4j - 3k.

A: Given: v=2i+3j-k  w = -2i - 4j - 3k.

Q: Find a nonzero vector orthogonal to the plane through points P(2,1,5), Q(-1,2,3), and R(0,3,3), and…

A:

Q: Verify that the two planes are parallel. -x + 6y + 2z = 4 + 3y + z = 5 Find the normal vector, n,,…

A:

Q: Find a vector parametrization of the line through P = (3, –8, 5) in the direction v = (-2, 0, 3)…

A:

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

A:

Q: · Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z…

A: Since r is the separation vector from the point x',y',z' to the point x,y,z and the difference…

Q: Verify that the two planes are parallel. -x + 6y + 2z = 8 -x + 3y + z = 9 2. Find the normal vector,…

A: Find your answer below

Q: Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector 10i – 2j +…

A:

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 7t, y = 7 -…

A:

Q: Find a vector v that is perpendicular to the plane through the points А %3 (0, 4, —3), В 3 (5, —5,…

A: Coordinator of the plane is given Find out the vector that is perpendicular to the plane

Q: Find the coordinates of a point P on the line and a vector v parallel to the line. X - 8 y + 2 = z +…

A: This question is based on 3-d coordinate geometry.

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: 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, 6, 3) and has the vector n = (1,6,…

A: I have stated the used formula in the solution.

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 5t, y = 9 –…

A: Let's find.

Q: Find a vector orthogonal to the line x+y=1

A:

Q: M contains the point with coordinates (0,0,1) 2 M is orthogonal to the vector 0

A: Introduction: The general equation of Plane is ax-x1+by-y1+cz-z1=0

Q: Find the coordinates of a point P on the line and a vector v parallel to the line x = 3 − t,   y =…

A: Given :              Vector v parallel parallel to the line x=3-t, y=-1+2t , z=-2.

Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 2 %3D y + 5 =…

A: The given question has been solved in detail.

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: Find a vector v that is perpendicular to the plane through the points A = (4, – 5, –2), B = (2,3,…

A: We are asked to find the vector that perpendicular to the plane through the points

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 7t, y = 4 -…

A: Given, The equation of the line x = 7t, y = 4-t, z = 3+9t We have to find the coordinate of the…

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: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 4 y + 7 = z +…

A:

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 8t, y = 8 –…

A:

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

A:

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 an equation of the plane that contains the point (-1, 2, 3) and is perpendicular to the line…

A: The plane is perpendicular to the line, then the direction vector of the line is normal to the…

Q: Find a vector perpendicular to the 2-space line: Qx - Ny + R = 0

A: Please see the below picture for detailed solution.

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 3t, y =…

A:

Q: find the vector equation of a plane that contains the intersection line of x + y + z = 1 and x – y +…

A:

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

A:

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

A:

Q: Find a vector parametrization of the line through P = (0, –8, 7) in the direction v = (7, 0, 0)

A:

Q: Consider the line L with vector equation (x, y, z) = (2,3,0) + t(1, 4, –1). Determine the point on L…

A: Foot of perpendicular is the closest point on the given line, Let M is the foot of perpendicular…

Q: Find the coordinates of the point P on the line and a vector v parallel to the line x = 3t, y = 1 –…

A: Given parametric equation of line x=3t, y=1-t, z=3+5t

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( 5 , −…

A:

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 5t, y = 9 -…

A:

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 6t, y = 8 -…

A:

Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 8 y + 3 = z +…

A:

Q: Find a nonzero vector parallel to the line of intersection of the two planes 5y – 4x + z =-1 and –…

A: The line of intersection of two planes is orthogonal to their respective normals.

Q: Consider a point Q(x1, y1, z1) and a line L given by the vector equation r = r0 +tv,where r0 =…

A: First obtain a, where a is the distance between R0 and Q.

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 8t, y = 5 -…

A:

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = (5, 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: (a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), 0(2, 0, – 1), and…

A: It is given that the plane contains  P(1,0,0), Q(2,0,-1) and R(1,4,3). Let, Equation of plane…

Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector