1. Find an equation of the plane that contains the line r = -2+ 3t, y = 4+2t, z = 3 - t and is perpendicular to the plane r- 2y+z = 5.

Q: 2. Find the equation of the plane containing the lines L1: (x-2)/2 = (y+1)/-1 = z/3; L2: (x+1)/2 =…

A: Given that:L1: x-22=y+1-1=z3L2: x+12=y-1=z+23

Q: 20. Find the point at which the line a = 1+ 2t, y = 4t, z = 2 –t intersects the plane r+y – 2z +1=…

A: Given that, equation of line:- x=2t, y=4t, z=2-t Equation of Plane:- x+y-2z+1=0

Q: 10. Find the coordinates of the point of intersection of the line L: x = -1+ 3t, y = 2 – 2t, z = 3 +…

A:

Q: (b) Find an equation of the plane that contains the line x = 1 + t, y = 2-t, z = 4 - 3t and is…

A:

Q: Calculate the equation of the line that passes through the point (0, 1, 2) that is parallel to the…

A: We need to find the equation of the line passing through a point, parallel to a plane and…

Q: Where does the line x = 2−t, y = 3t, z = −1 + 2t intersect the plane 2y + 3z = 6?

A: Where does the line x = 2−t, y = 3t, z = −1 + 2t intersect the plane 2y + 3z = 6? Given x, y, z in…

Q: 4. (a) Show that the line l given by l: 1= 2+3t, y=1+4t, z= 5+ 2t, te R, lies in the plane II given…

A: Given problem:- Show that the line  given by   l : x = 2 + 3t , y = 1 + 4t , z=5+2t ,t in R   lies…

Q: 3. Find the plane determined by the intersecting lines L: x = -1+t, y = 2+t, z = 1- t; L2: x = 1 -…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the point at which the line x=1+t, y=3-2t, z=1-t intersects the plane 2x+3y+3z=0

A:

Q: Is the line x = 4 + 2t, y =-t , z=-4t - 1 parallel to the plane 3x + 2y + z = 7 ?

A:

Q: 4. Give the general equation of the plane containing the point (3,-1,4) and 2- z perpendicular to…

A:

Q: 24. The plane that contains the line x = 1 + t, y = 2 – t, z = 4 – 3t and is parallel to the plane…

A: To find out equation of plane first we change the equation of line in symmetrical form then find out…

Q: (b) Calculate the distance from the point P(3,–1, 2) to the plane with equation 2x – y +z = 4.

A:

Q: 2. Find an equation of the plane that contains the line r = 1 +t, y = 2 - t, z = 4 – 3t, and is…

A:

Q: Find the point at which the line intersects the given plane. x = 3 - t,   y = 3 + t,   z = 2t x - y…

A: Substitute the line equation in the plane equation

Q: Is the line x = 1 + 2t, y =-2 + 3t, z =-5t related in any way to the plane -4x - 6y + 10z = 9? Give…

A:

Q: Find the point of intersection of the line x-9 = - 5t, y +1= -t, and the plane 2x – 3y + 4z + 7 =0-…

A:

Q: Find an equation of the plane that contains the line x = −2 + 3t , y = 4 + 2t , z = 3 −t and is…

A:

Q: Find the equation of a plane that passes through the origin and contains the line x = 2t, y = 3t, z…

A: Consider the provided question, The equation of a plane passing through the point (x1, y1, z1) is…

Q: Find the distance between two lines (L1: x=3t-1, y=t+6, z=2t+3 and L2: x=2t+6, y=2t+11, z=-t+3)…

A:

Q: Find the point at which the line 7(t) = (5, – 3, - 6) + t( – 2, - 8, 6) intersects the xz plane.

A:

Q: Q1. A) Determine if the plane given by -x + 2z = 10 and the line given by %3D (x = 5,y = 2 - t,z =…

A: Consider the given values. -x+2z=10 And, (x=5, y=2-t, z=10+4t)

Q: 25. Find an equation of the plane through the line of intersection of the planes x – z = 1 and y +…

A: Equation of a plane P that passes through the line of intersection of two planes P1 and P2 is given…

Q: find the point in which the line meets the plane x = 1 - t, y = 3t, z = 1 + t; 2x - y + 3z = 6

A:

Q: Suppose we need to find an equation of the plane that passes through the line of intersection of the…

A: Since, we know that equation of a plane passing through the intersection of planes P and Q is given…

Q: Determine the point of intersection of the line and the plane. e:[x, y, z]= [3, 1, 2]+t[1, -4, -8]…

A: Finding the general point in the line substituting in the equation of a plane

Q: Find the point at which the line (4, –1, 4) + t(4, 2, 3) intersects the plane 4x 5y + z = 88.

A:

Q: Find the general equation of the plane containing the point (2, –1,4) and normal to the line 2 = =…

A: As the line is normal to the plane, the DRs of the line and normal of plane is same.

Q: 2) Find the equation of the plane that is orthogonal to the planes 3x-2y-2z=1 and x-3y-10z = 4 and…

A: Given: The equation of two planes 3x-2y-2z=1 and x-3y-10z=4 and the equation of one line…

Q: Find the points of the intersection of the line x = -2, y = 4+2t, z = -3+t with the xy-plane,…

A: Given, The line x = -2,  y = 4+2t ,  z = -3+t   We have to find the points of intersection of line…

Q: Find an equation of the plane that passes through the line of intersection of the planes ( x – z = 1…

A: We have found the plane that passes through the line of intersection of the planes x-z=1 &…

Q: Find the equation of the plane containing the line: x = 2 + 10t, y = 2 – 2t, z = 9 + 4t and parallel…

A:

Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

A:

Q: The intersection point of the line whose equation is (x+2y+z=1),(x+y+2z=-1) with the xz plane is:

A: we have given x+2y+z=1  ...(i)x+y+2z=-1  ...(ii)solve it  2×(i)-(ii)x+3y=3   ...(a) this is equation…

Q: Show that the line in which the planes x + 2y – 2z = 5 and 5x – 2y - z = 0 %3D intersect is parallel…

A:

Q: Check that the line (1,0,1)+t(3,0,1) is parallel to the plane -2x+4y+3z=13 and calculate the…

A: For the equation of the plane , the direction vector of the normal to the plane is given by . For…

Q: Find the point in which the line through the origin perpendicular to the plane 2x - y - z = 4 and…

A: Your line, perpendicular to the plane will have the slope of <2, -1, -1>, and passes through…

Q: Consider the plane P with equation −2x+2y−z = −5 and line L with equations x = 9−4t y = −5+2t z =…

A: Consider the plane P with equation −2x+2y−z = −5 and Line with equations x = 9−4t y = −5+2t z = 4−6t

Q: 1. Determine the point of intersection of the line and the plane if it exists. π: 7x+y+ 5z = 0 x-4…

A:

Q: Consider the plane P with equation −2x−2y+z = 1 and line L with equations x = 2−3t y = 9−6t z = −4…

A:

Q: Find the point at which the line intersects the given plane. x = 3 - 3t, y = 4t, z = 1 + t; x + 2y -…

A: Given line ,x=3-3ty=4tz=1+t   -1and plane , x+2y-z=6

Q: Find the point at which the line intersects the given plane. x = 4 - t, y = 5 + t, z = 3t; x - y +…

A:

Q: Show that line y+1 is parallel to plane x- 2y + z = 6 С.

A:

Q: Consider the plane P with equation x+2y+2z=-7 and line L with equations x=-4-2t y=4+7t z=-1+3t…

A:

Q: If the line L: X = 3 + 2t , Y= 2t , Z = t intersects the plane X+ 3y - Z =-4 in a point P. The…

A:

Q: Determine the Cartesian equation of a plane that is perpendicular to the plane x - 2y + z = 6 and…

A: Given : A plane x-2y+z=6 and which contains a line -x+2-3=y+1=z+12  To find: The Cartesian equation…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.