Consider the line that contains the point (2, -3, 5) and that has the direction vector (1, 2, 4). a) Write the point form of the line. b) Determine the point at which the line in part (a) intersects the plane 2x - y + 5z = -8.

Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

Q: Find any line equation that does not intersect the plane 2x – 5y + 3z 4. -

A:

Q: Find an equation of the plane through (-7, 2, 1) that is 2 = 3t, y +3 = 6t, z = perpendicular to the…

A: We know that equation of plane passing through the point (x1,y1,z1) and normal n=ai+bj+ck is…

Q: Show that the lines determined byr 1(t) = <−2 − 5t, 3 + 2t, 4t >andr 2(t) = <8 + 15t, 1 −…

A:

Q: Find the distance between line 1, and the plane parallel to it and containing line I, where 4:…

A:

Q: The plane with equation:

A: Given, the plane with equation:                        r→=(1, 2, 3)+m(1, 2, 5)+n(1, -1, 3)…

Q: Determine the symmetric equations of line that passes through the points B and С.

A:

Q: find the distance from the point to the plane. (2, -3, 4), x + 2y + 2z = 13

A: Given:

Q: Which point is closest to the yz-plane? ? What is the distance from the yz-plane to this point?

A: The distance of a point from the yz-plane is given by the x coordinate of the point. Because, the x…

Q: Find the equation of a plane bisecting the line segment joining (2,0,6) and (6,2,4) and…

A:

Q: Plot the planes given by the equations y z = 0 and x = 0 and their line of intersection using a box…

A: The given planes are y-z=0 and x=0. Hence the line of intersections of these two planes can be…

Q: Give the equation of the line in vector form, parametric form and symmet The line through the point…

A:

Q: Find the distance from the point A(2,4,3) to the plane determined by the three points B(1,4,2),…

A:

Q: Parametrize the line segment joining the points P(1, 2, 0) and Q(1, 3, -1).

A: We know that equation of line passing through the points (x1,y1,z1) and (x2,y2,z2) is

Q: Find the distance from the point (3, -4, 2) to the yz-plane

A: We have to find the distance from the point 3,-4,2 to the yz-plane. We know that if any point px,y,z…

Q: Find the vector, parametric, and symmetric equa lines: (a) the line perpendicular to x+7_y-4 with 3…

A:

Q: Determine the intersection of the perpendicular line drawn from the point A (-5, 3, 7) to the plane…

A: The equation of the plane is given as, v=0,0,2+t1,1,3+s2,0,-3 Or…

Q: if (u, v) and (s, t) are two distinct points in the plane, what is the distance between them?…

A:

Q: the coordinate plane be

A:

Q: Find the plane determined by the intersecting lines.

A:

Q: Find an equation of the plane through (1,8, 5) that is perpendicular to the line x – 2 = 3t, y + 3 =…

A:

Q: Determine whether the line L: = 3- 2t, y=4+ 2t, z = 5+ 2t. is parallel to the plane a-y+3z 7.

A:

Q: Give the parametric and symmetric equations of the line that passes through the point (4, –3,5) and…

A: we have to find the equation of line which is passes through the given point and perpendicular to…

Q: Do three points determine a plane?

A: We know by following ways plane can be determined: 1. Three non collinear points determine the…

Q: Find an equation of the plane through (4, 5, 7) that is - 2 = 5t, y +3 = 10t, z = -5t. perpendicular…

A:

Q: What does the cross product of two planes that intersect at a line represent in terms of the line of…

A: Firstly, let us understand what a normal vector is. Normal Vector of a plane is a vector which is…

Q: the distance between point and our plane is (-3, 3, -2) and not (-3, -3, -2)?

A:

Q: Find general point for the lines The line through (0, -7, 0) perpendicular to the plane x + 2y + 2z…

A:

Q: What is the distance from the point (1,9,3) to the xz-plane?

A:

Q: Consider the points P(-4, 1, 0, 3), Q(0, 3, 1, -4), R(-2, 1, 5, 0). RS PQ is parallel to Find the…

A: Given:- P=(-4,1,0,3) ,Q=(0,3,1,-4) and R=(-2,1,5,0) To find the point S in R4 whose third component…

Q: Find the distance from the point Q(6, -2, 4) to the plane 2x - y + 2z = 4.

A: It is given that a point Q6,-2,4 and equation of the plane 2x-y+2z=4. Here, x1=6, y1=-2, z1=4  and…

Q: -6x - Find dA, where Ris the parallelogram enclosed by the lines -3x+y R – 6x – y = 0, – 6x – y = 2,…

A: I have used jacobian to solve the area of above double integral.thanks

Q: he intercepts of the plane given by

A: Intercepts of the plane are (3,5,3).

Q: Find an equation of a line containing the point (1, 7, -3) and parallel to the yz- plane.

A:

Q: Consider line L of symmetric equations -x-2-y , Find point P that belongs to the line and direction…

A: Consider line L of symmetric equations -x=-2-y=z2

Q: Find the distance from the point (3, 1,0) to the line given by symmetric equations *** =-3, y= 1.

A: Given that: The point is: (3, -1, 0) and equation of line is:         x+42=z-3, y=1

Q: Find the equation for the plane through Po(-5, - 8,8) perpendicular to the following line. x= - 5-t,…

A:

Q: Show that the plane whose intercepts with the coordinates axis are x = a, y =b, z c has equation :…

A: Consider an equation of plane as It is given that the intercepts of plane are x=a,y=b and z=c. So,…

Q: Find an equation of the plane through (4, 1, –4) that is perpendicular to the line x – 2 = 5t, y+3 =…

A:

Q: Find the distance from the point (-2, 1, 4) to the plane x = 3

A: Given: The point -2,1,4 and plane x=3 To find: Distance from the given point to the given plane.

Q: Describe a method for determining whether four points P , Q , R , and S , lie in the same plane

A: We know that if some points lie on the same plane, then their slope would be same.

Q: Parametrize the line segment joining the points P(-3, 2, -3) and Q(1, -1, 4)

A: we have to parametrize the line segment joining the points P(-3,2,-3) and Q(1,-1,4)   as we know…

Q: Show that the sum of the squares of the direction cosines of a line through the origin is equal to 1…

A: To show: The sum of the squares of the direction cosine of a line through the origin is equal to 1.

Q: Find the distance from the point (-2, 1, 4) to the plane y = -5

A: Given plane is: y = -5 Given point is: (-2, 1, 4) We know that the distance (d) of a point P(h, j,…

Q: Do two intersecting lines determine a plane?

A: Two lines intersect at only one point.

Q: Give the parametric and symmetric equations of the line that passes through the point (5,−1,3) and…

A:

Q: how do i prove that the diagonals of a parallelogram bisect each other ? Then have to name…

A:

Q: Find an equation of the plane through (-4, 3, –8) that is perpendicular to the line x – 2 = t, y +3…

A: Given line : x-2=t , y+3=2t ,  z=-tx-21=t , y+32=t , z-1=tx-21= y+32= z-0-1 comparing with standard…