Find the intersection point(s) (if any) of the line r(t) = (21,-14, -9) + t(2,3,4) and the plane 19 x 15y + 6 z = 538. Point of intersection: (

Q: Find the point, P, at which the line intersects the plane. x= - 3+ 10t, y = 9- 9t, z= 9- 7t; - 10x +…

A: The objective is to find the point of P, at which the line intersects the plane.

Q: Find an equation for the plane through the point (0, –4, 5) which is perpendicular to the line…

A:

Q: Find the distance from the point (7, -14, -21) to the plane:  2x - 3y - 6z = 1

A:

Q: (b) Describe the relationship between each pair of planes, and determine any intersection (iii)…

A:

Q: bugi nе pom the equa that passes 2,1), 2(0, 2, 3) the d P3(−2, −1, −5). Then, find the distance from…

A:

Q: Find the characteristic polynomial of the matrix, using either a cofactor expansion or the special…

A:

Q: (x = t r:{y = -t (z = 1+ 4t concurrent, and if so, determine the point P common to them. Check if…

A: Let the equation of a line passes through the point x0,y0,z0 with the direction vector v→=l,m,n be…

Q: Determine the line of intersection between the following planes 12. 5x+2y-7= 9 and -2x+8y +9= = 3.

A: Given: The planes are 5x+2y-7z=9 and -2x+8y+9z=3 To find the line of intersection of the given…

Q: Determine if the line given by r(t)=(-2t, 2+7t, -1-4t) intersects the plane given by 4x+9y-2z =-8…

A:

Q: Q2. Find the equation of the line that passes through the point (-3,2,-1) and parallel to the line…

A: Given point is (-3,2,-1). And the planes are,

Q: Find the intersection of the line and plane: 3z (2x + y) = -5, P = ( r(t) = (3,-1,0) + t (-3, -2,…

A: Given line : r(t)= (3,-1,0)+t(-3,-2,-1) Given plane : 3z-(2x+y)=-5                       2x+y-3z-5=0…

Q: Determine whether the two planes x-y + 2z = 1 -x-y +z = 3 are parallel or intersecting. Find their…

A:

Q: Find the point of intersection of the two lines l1 : 7 Intersection point:

A: Introduction: The point of intersection is the intersection of two lines or curves. A point is the…