Let P be the like (-1,0,2) . Consider the plane that goes through the points A=(3,4,-1), B=(1,-3,3) and C=(1,2,0). a) find a vector equation for the plane that goes through the point P and is parallel to the plane that goes through the points A , B and C. b) find a point- normal equation for this plane ( the plane that goes through P and is patella to plane that goes through the e points A,B and C).

Q: be the line through the point with coordinates (0,1,0) in the direction of the vector h of the…

A:

Q: Write the scalar equation of the line given the normal vector point Po(-2,-4). n = and a

A: Scalar equation of a line is given by , Ax+By+C =0, where (A,B) are the cordinates of normal vector…

Q: Let L. be the line passing through the point P=(5, 1, 1) with direction vector [-1,5, -2], and let T…

A: Solution :

Q: Let L be the line with parametric equations x-2-2t y-10-2t 2-8-21 Find the vector equation for a…

A:

Q: Let A= (-1,3,3) B= (4,-1,0) C= (5,4,-7) D= (2,-1,-1) i) the normal vector to the plane ABC. ii) the…

A:

Q: Determine vector and parametric equations for the line in R that passes through the points A(1,0, 1,…

A:

Q: Find the vector n= normal to the plane passing through the points (0, -3, 0), (2, -1, 0) and (-2,…

A:

Q: b) Find parametric and vector equations for the line through (2,3,0) perpendicular to the vectors u…

A:

Q: Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector…

A:

Q: Find an equation for the plane that passes through the point (3, -2, 1) normal to the vector n = 2i…

A: Given:A point (3, -2, 1) normal to the vector n = 2i + j + kThe normal vector can be written as,

Q: Determine the equation of the plane with a point 'a' and the normal vector 'n': a = (−1, 2, −3)t ,…

A:

Q: Find parametric equations for the line through p (2,3,0) and perpen-dicular to the vectors u =(1,…

A:

Q: Calculate the distance from point B=(−1,3,−1) to the plane that passes through point A=(3,2,−1) and…

A:

Q: Find the projection of v = [-3, 3, 6] onto the line L with vector equation x=td where d = [4, -3, 1]

A:

Q: Find an equation of the plane that passes through the point Po(0, -2,3) with a normal vector n =…

A: To find the equation of a plane that passes through the point with a normal vector , you can use…

Q: P(2,5, 4) and Q(8,3,3) Let be the line through P in vector direction (1,2,3) and let II be the plane…

A: