let 4:x = --t, y=+t, z =+t L2:x = 2 +t, y = 3 +t, z = 1+t M: 3x + y- 2z = 3 straight lines in space and let's have the plane 1) Find the magnitude of the included .M and the plane L1 anale between the straight line . L2 and L What is the relationship between the straight lines

Q: 5) Find the equation for the plane perpendicular to the plane P and containing the line L, where P:…

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Q: ax + by + cz + d, = 0 13) Show that the distance between the parallel planes: and ax + by + cz + dz…

A: here we have to prove the formula of distance between 2 parallel planes.

Q: Let L4:x = -+ t, y=}+ t, z = }- t L2:x = 2 + t , y = 3+t, z = 1 +t Two straight lines in space and…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Find point P where the given line intersects the given. Plane or decide that the line aoes not…

A: For finding intersection point, substitute the values of x, y, z given in equation of line in…

Q: Find the distance from the point (- 5, 20, – 7) to the given plane or axis. If required, round your…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Q7. What angle does the line of intersection of the plane O make with the nonnegative 2x + y - z = 0…

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Q: Find the intersection of the planes P1  and P2. P1: has equation (x−2)+2(y−3)+3(z−4)=0 P2: is…

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Q: e the line defined as 3 – 3t, y = -5+t, z=a+bt, teR e the plane defined as D: 4x + 3y + z = 7. e…

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Q: let L4:x < = -+t, y=+t, z=-t STRAIGHT IN SPACE AND LET'S HAVE A LEVEL L2:x = 2 + 2t , y= 3 – 2t, z…

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Q: Determine whether the plane x + y + z = 9 and the line x = t, y = t + 1, z = t + 2 are parallel,…

A: Given: The planes x + y + z = 9 and the line x = t, y = t + 1 , z = t + 2.   To determine Whether…

Q: Let a and b be real numbers. Let L be the line defined as L:x = 6 – 6t, y = -11+t, z= a+ bt, teR %3D…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Let L be the line x = 3t + 1, y = −5t, z = t. (a) Show that L lies in the plane 2x + y−z = 2. (b)…

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Q: Find the distance from the point ( - 4, 21, – 19) to the given plane or axis. If required, round…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Consider the line which passes through the point P(3, -1, -1), and which is parallel to the line x =…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A: A detailed solution is given below

Q: Let a and b be real numbers. Let L be the line defined as L :x = 5 – 5t, y = -9 + t, z = a + bt, teR…

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Q: Find the point where the given line intersects the given plane x = 1-t, y = t, z = 1+t, z = 1- 2x +y

A: Given lines, x=1-t , y=t  , z=1+t  Given plane, z=1-2x+y To find the point where the given line…

Q: Consider the plane P with equation 2x-2y+z =4 and line L with equations x= 3+2t y =-1-5t z= 5+4t…

A: Solved below

Q: Let L,:x = 3t +5, y = 2+t, z = 2+ 3t L2:x =t - 2, y = t + 1, z = 1-2t Two lines in space and let's…

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Q: Let a and b be real numbers. Let L be the line defined as L:x = 4 – 4t, y = -7+ t, z= a+ bt, t e R…

A: Given line is  L: x=4-4t, y=-7+t, z=a+btl→=(-4, 1, b), p→=(4, -7, a) Where l→ is direction to which…

Q: Find the point at which the line intersects the given plane. x = 4 – 4t, y = 5t, z = 1 + t; x + 2y -…

A: We have to find the point at which the line intersects the given plane.

Q: . Find the relation between line L and plane P: Question 9. 2x +2y-32-1=0. If they intersect at one…

A: The given plane is 2x+2y-3z-1=0. Find the relation between line L and plane P. 1. The given line is…

Q: Find the distance from the point Q= (2,2,2) to the line of intersection of the planes x+y+z=1 and…

A: Distance from the point Q(2,2,2) to the line of intersection of planes x + y + z = 1 and x + y = 2

Q: 4. Consider plane P: 4x – y+ 2z = 8, line l: (x, y, z) = (1+t, –1+ 2t, 3t ), and point Q(2, –1,3).…

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Q: A line has parametric eauation s: x = 8 – 21, y = -9 + 3t, z = 6 – t At what time does the line…

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Q: nd the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Let a and b be real numbers. Let L be the line defined as L: x = 6 – 6t, y = -11+t, z = a + bt, t eR…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: 7. Find the dis to the plane x +2y+ 6z = 10 %3D 8. Find the angles between the planes a+y= 1,…

A: According to guidelines we should have been able to solve only one question at a time #8

Q: 3. Consider the plane TT: 4x + 3y - 2z + 12 = 0. What is the relationship of the plane to each of…

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Q: e. The plane through Po(2, 4, 5) perpendicular to the line x = 5+ t, y = 1 + 31, z = 4t

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: 2. Assume that the plane P3 is perpendicular to the yz-plane, and the line l2 : x = 2t, y = t, z =…

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Q: L:x= 2t, y= 2-t, z 2-t L2: x = 1-t, y = -3-t, z = 1-t M:x + 2y-z 3 straight in space and let's ha 1-…

A: The parametric equation of the line L1: x=2t, y=2-t, z=2-t L2: x=1-t, y=-3-t, z=1-t and the plane M:…

Q: (2t+l, st-5, lot ) f 4z: Given two lines ( 34, 2++3, zt+1) located in Sice the plane ? plane, find

A: The required equation for the plane is calculating by the below method.

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

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Q: Q1): Find the point (x, y, z) that lines on the plane x +y + 2z = 4 that is nearest to the origin.

A: This question can be solved using the concept of distance of point from a plane in three dimensional…

Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A: Given:   Plane→   2x+3y = 10  Line→       x-1 3= y+1-2 = z-9

Q: Consider the plane P with equation −2x−2y−z = −11 and line L with equations x = 1−3t y = −1−6t z = 2…

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Q: 6. Given the plane n1 and n2 defined as follows: T: : 2x + 5y – 72 +2 = 0 T2:x+y-z+3 =0 a-)…

A: In this question, the equations of two planes are given. We need to find the dihedral angle between…

Q: giren points wll, 2), x (4,-3), y (-6, +) and z (-4, +) cartesjan plane on Since tnow that A Cb), B…

A: To find:- How opposite and adjacent sides related to given slopes  And What specific geometric…

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: Find the distance from the point (– 4, 21, - 5) to the given plane or axis. If required, round your…

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Q: et L be a line which passes through the point (-3,0, 1) and is perpendicular to the plane z +…

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Q: What is the equation of a plane whose r-intercept is a, y-intercept is b, and z-intercept is c?…

A: Solve for the equation

Q: Let S be the plane with the equation x + y – 3z – 6 = 0. - Find the distance between this plane and…

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Q: Find the distance between the origin and the intersection line of the planes : 2x+y+z=2 and x+2y+z=3…

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Q: Consider the plane II : 2x – y+ z= 1 and the line l : (a) Find the intersection point of the plane…

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Q: Find the acute angle of intersection of the planes x + 2y – 2z = 5, 6x – 3y + 2z = 8 to the nearest…

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Q: Find the point(s) of intersection (if any) of the plane and the line. (If an answer does not exist,…

A: Given line x-38=y2=z-714=tAny point on the line is of the form,x=3+8t,y=2t,z=7+14t,Put…