Suppose that the line e is represented by r(t) = (10+ 2t, 14 + 6t, 23 + 8t) and the plane P is represented by 3x + 4y + 5z = 26. 1. Find the intersection of the line e and the plane P. Write your answer as a point (a, b, c) where a, b, and c are numbers. Answer: 2. Find the cosine of the angle 0 between the line e and the normal vector of the plane P. Answer: cos 0 =

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: Find two di¦erent planes whose intersection is the line x = 1 + t, y = 2 - t, z = 3 + 2t . Write…

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

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Q: Find an equation for the plane that contains the line v = (-1, 1, 2) + t(9, 5, 4) and is…

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Q: Find the distance, d, between the point S(4,8,4) and the plane 8x + 7y + 3z = 40. The distance, d,…

A: Given:       Point =S4,8,4        Plane 8x+7y+3z=40                  8x+7y+3z-40=0 Distance between…

Q: Determine whether the planes 3x + 2y − z = 7, x − 4y + 2z = 0 are parallel, orthogonal, or neither.…

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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: the Find the distance bebween point of inter Section of the Line %3D X -y -Z =2, 2 x +34 -7Z = -1 |…

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Q: Determine whether the planes 5x − 3y + z = 4,  x + 4y + 7z = 1 are parallel, orthogonal, or neither.…

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Q: Which of the following is the equation of a plane parallel to the cz-coordinate plane and passing…

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Q: On the line of intersection of the planes y+2z=12 and x+y=6, find the point (a,b,c) that is closest…

A: Given planes, y+2z=12andx+y=6 Consider the point of intersection be x,y,z.

Q: 4. Determine whether the planes are parallel, perpendicular or neither. If neither, find the angle…

A: Two planes are neither perpendicular nor parallel.

Q: If the plane ar + by + cz = 30 through the points P(4, 1, 2) and Q(2, 3, – 1) is orthogonal to the…

A: Given plane passing through the given point P and Q

Q: O Find an equation for the plane throught (l,-l,3) parallel to the plane 3x+y+Z=7

A: 1) To find the equation of the plane passing from (1,-1,3) and parallel to the plane  3x+y+z=7

Q: Which of the following is the intersection point of the plane 5x- 2y- 3z=0 and X = 6+ 2t the line y…

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Q: Consider the line L(t) = (-5 – 3t, –1 – 4t,4+5t). Then: L is ? to the plane 7y – 21x – 7z = 63 L is…

A: Given the line  L(t) = -5-3t, -1-4t, 4+5t ⇒ L(t) = -5, -1, 4 + -3t, -4t, 5t ⇒ L(t) = -5, -1, 4 + t…

Q: You are given the following points: A = (11, –14, –16), B = (16,0, 5), C = (-9, 16, 13). Which point…

A: Answer

Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z -12…

A: the point at which the line meets the plane is (x,y,z) = (2,-207,277)explanation is given in below…

Q: Given the planes π1 : x − 2y + 3z + 1 = 0 and π2 : 2x + y + z + 2 = 0. Find the equation of the…

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Q: b) Obtain the equation of a plane, P that is orthogonal to the line L:x=1+4, y=8+1, z =9+9t_and goes…

A: Given line is                                       L1:x=1+4t, y=8+t, z=9+9tvector parallel to line…

Q: 0- Draw a sketch of the Plane of 4x-tyt22-9=0

A: Solution

Q: Given that the plane A with the equation x - 2y + 3z = 1 and the plane B with the equation x + y + z…

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Q: 1. Consider the planes P and Q given as 2x- 3y +2 = 3 and 4x- 6y + 22 = 5. Are P and Q parallel?…

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Q: Find an equation for the plane parallel to the liner =1- 21, y = 2 + 3t %3D 2 = 1+ 2t and that…

A: Given: Plane is parallel to the line x=1-2ty=2+3tz=1+2t Also, the plane contains the line of…

Q: Find the point​ (if it​ exists) at which the following plane and line intersect. y=−11​;…

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Q: To which coordinate plane is the plane y = 1 parallel?

A: y=1

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

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Q: 7x + 3y + 4z = 5, and 21x + 9y +12z = 13

A:

Q: Show that the line x = −1 + t, y = 3 + 2t, z = −t and the plane 2x −2y−2z + 3 = 0 are parallel, and…

A: Here we have to show that the given line,  x=-1+t, y=3+2z, z=-t and plane 2x-2y-2z+3=0 are parallel…

Q: Consider the line L(t)=⟨4t−1,2−5t,−3−4t⟩. Is L parallel, perpendicular, or neither to the plane…

A: Lt=<4t-1 , 2-5t , -3-4t >Direction ratio of Lt=< 4 , -5 , -4 >Normal vector to given…

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: Consider the lines x – 4 l2 : 4 - 1 l1: x= 4 – 3t, y = 2t, z = 1 + 5t , %3D 2 (b) Find an equation…

A: Given that:                        Two lines are: l1: x=4-3t, y=2t, z=1+5t,  l2:x-44=y1=z-12

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: Determine the Point OF 3x +y+22 = 45 and the Line witth plaremetre eg dartons 1 = 1+t, y= 3 +2 € ,…

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Q: The distance from the point P(2, 1, 0) to the plane 2x + y + 2z+ 6 = 0 is 3.7 True O False

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Q: the plane whose intercepts with X zagy = b,Z=C show that the Coordinate axes are has equation Ą + +…

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Q: (A) Find the Distance between the point (x.y.z) and the plane 3x+2y+6z = 6 8 If the plane meet with…

A: As per the company policy i can answer only first question for you, More than that leads me towards…

Q: Find the distance from the line x = 2 + t, y = -2+ 2t, z = 4 – t and the plane 2x – 3y – 4z = 12…

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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 cosine of the angle, 0 Ses x/2, between the plane x +2y-2z= 2 and the plane 4y-5x + 3z =…

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Q: 4. Determine whether the planes are parallel, perpendicular or neither. If neither, find the angle…

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Q: Determine whether the planes 2x − z = 1, 4x + y + 8z = 10 are parallel, orthogonal, or neither. If…

A: 2x-z=1,  4x+y+8z=10 Now comparing with a1x+b1y+c1z=d1  &  a2x+b2y+c2z=d2, we get a1=2, b1=0,…

Q: Given that A and B are parallel to the yz plane, that |A| = 2, |B| = 4, and A • B = 0, what can you…

A: Consider the provided question, Given A and B are parallel to the yz plane.

Q: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Q parallel? Find…

A: Consider the planes P and Q given as 2x-3y + z = 3 and 4x- 6y + 2z = 5: Are P and Qparallel? Find…

Q: x + 4y + 2z = 4, and 4x -3y +4z = 7.

A: Topic - plane and vectors

Q: Suppose the plane II is given by the equation A + By +7z = 8, and it is parallel to the lines l1, 2…

A: It is know that if the two vectors are parallel then their dot product is 0. Determine the direction…

Q: x + 13y + 7z = 4, and 2x + 26y + 7z = 8

A:

Q: For what positive value of c is the acute angle between the plane containing the points A(0,0,1),…

A: Calculate the vector normal to the yz plane. Equation of yz plane:x=0Equation of vector normal to yz…