Find the equation of a plane containing point R(1,0,1) and parallel to the plane 2x-y+z=1. a direction vector for the given plane is v=<2,-1,1> a plane that is parallel to this plane will have a direction vector that is a scalar multiple of v so we can choose 1 as that multiple, so a plane that is parallel to the given plane that contains the given point is: 2(x-1)-(y-0)+(z-1)=0 2x-2-y+z-1=0 2x-y+z=3 is that correct?

Q: 2. Find an equation (parametric and vector form) of the line if the line is perpendicular to the…

A:

Q: Find an equation of a plane containing the line r (-3, -3, -5)+t(4, 4, -2) which is parallel to the…

A: A plane containing the line r=-3, -3, -5+t4, 4, -2 which is parallel to the plane -2x+y-2z=8. We…

Q: Determine a vector equation for the line that is perpendicular to 7 = (4, 1) + s(−3, 2), sER, and…

A: We need to find the equation of line perpendicular to r→=(4, 1)+s(-3, 2),  s∈ℝ and passing through…

Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 &amp; C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: Find a scalar equation of the plane containing the line and the point (-5, -1,5). x = 6 +8t, y=-1-3t…

A:

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

A:

Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

A:

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

A:

Q: 2. Find the equation of the planes: a) (in general form) that goes through the three points A(4, 0,…

A:

Q: - 3)² = 81 then, find its ce or a=<3, -1

A: 1. Given: The points are 2,3,-6 and -1, 4, 5 To find the distance between the given points. The…

Q: Find the vector equation of the line that contains the points (-17, 10,2). r(t)= ( ) +t ( and

A: Answer :

Q: Determine the point at which the line passing through the points P(1, 0, 6) and Q(7, -1, 7)…

A:

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

A: Given:equation of two planes To find:vector equation of line that intersects these planes

Q: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…