(b) A rectangle defined by four points A(0, 0, 0), B(2, 0, 0), C(2, 2, 0) & D(0, 2, 0) is rotated 45° about a line L= 2i + 3k. Find the coordinate of the rectangle after the rotation.

Q: 16. What is the image of (2, -2) rotated 270° counterclockwise about the origin? А (-2, -2) в (-2,…

A: Solution

Q: 11. Find parametric equations for the line that contains the points P(2, -4, 7) and Q(0, –3, 5).

A: If Px0 ,y0,z0 and Qx1,y1,z1 are any two points then the parametric equation of the line containing…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: 4. A carnival ride is drawn on a coordinate plane so that the first car is located at the point (30,…

A: Coordinate point is (30,0) Rotation is 270 degrees.

Q: When the 2-dimensional shape shown below is rotated about the axis indicated by the dashed line, a…

A: When a 2 dimensional shape is rotated about an axis, a 3 dimensional shape is formed

Q: Find parametric equations for the lines in The line through (2, 4, 5) perpendicular to the plane 3x…

A:

Q: 2 -10 -8 -6 -4 -2 2 8 -2 C hp -> 4. 6, Co

A: topic - rotation of a rectangle around origin

Q: (d) Find the parametric equation for the line segment from point P(1,3, 2) and Q(1, –1,6).

A:

Q: D) Find the parametric and symmetric equations of the line through the points(1, and (-5, 4, 2).

A: Given query is to find the equation of the line.

Q: Find the image of the point A(-2, 4, 5) under a rotation of 60 degrees In the plane x = 2 about the…

A: We need to find image of given point.

Q: Find parametric equations of the line that is perpendicular to both i = (1,0,0) and i = (1,1,1) that…

A: Given that: i=<1, 0, 0>v=<1, 1, 1>and P(1, -2, -1)

Q: 2. Find the parametric equations of the line passing through the point (-1,4, -3) and is parallel to…

A:

Q: Find the parametric equations of the line segment that passes through the points A(4,2,-5) and…

A:

Q: 4 -8 -6 -4 -2 2 4 8 10 E,

A: Given query is to find the image points after 180° counter clockwise rotation.

Q: Find parametric equations for the line through P(8, −7, 9) perpendicular to the vectors A = ⟨3, −1,…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  given vectors are

Q: 1. Write vector and parametric equations of the line. a) parallel to the line x+6y = 1 and through…

A: Parametric and vector equation of line

Q: Find the parametric equations and the symmetric equations of the line that passes through the points…

A: Given: A line is passing through the points P-1, 4, 3 and Q8, 10, 5.

Q: What must be the equations of the rotation about the point (1, -1) at an angle e=90°? O x' = y , y'…

A:

Q: bz+ bz=c, b0, be a line in the complex plane, w the reflection of the point through the line then

A:

Q: the point c (-3 -1) is rotated 180 degrees clockwise around the orgin. What are the coordinates of…

A:

Q: The parametric equation of a line passing through A(1,1,1) and B(-1,2,0) is

A:

Q: Find an equation of the plane passing through the point perpendicular to the given vector or line.…

A:

Q: 5. Find the parametric equation of the line passing in R³ passing through the points (3, 1,0) and…

A: Directly use the formula for the parametric equation in R3

Q: Find an equation of the plane passing through the point perpendicular to the given vector or line.…

A: Given point is (0,4,0) and normal vector is -7i+5j.

Q: Find parametric equations for the lines in The line through P(-2, 0, 3) and Q(3, 5, -2)

A: To find the parametric equation for PQ

Q: 6. Find the image equation of the line -2x +y + 3 = 0 under the rotation about C = (1, 1) at an…

A:

Q: Find parametric equations for the line containing the points P(0,2,0) and Q(1,3,5).

A:

Q: Find the parametricequations of the line passing Through (-2,0,3) parallel to ū = 2i +49-2R.

A:

Q: a) Find the distance from a point (3,5,6) to a plane 2x + 3y + 5z = 1 b) Find the angle between the…

A: Find the distance of the point to the plane and find the angle between the given planes.

Q: coordinates of A(-11.5, 9), B(14, 8), and C(6, -7). What are the coordinates of its image after a…

A: Given data:     The first point is: A=(x1,y1)=(-11.5,9). The second point is: B=(x2,y2)=(14,8). The…

Q: What is the image equation of the line 2x+y-1=O under the rotation about the point (1, -1) at an…

A:

Q: Determine the angle of rotation necessary to transform the equation in x and y into an equation in X…

A:

Q: Find parametric equations for the lines in The line through (1, 1, 1) parallel to the z-axis

A: Given: 1,1,1 parallel to z-axis

Q: 3. Find the parametric equation of the line passing through the point (-1,0, 3) and in the direction…

A: Equation of the line passing through the point (-1,0,3) in the direction N(7,0,-2) is   ( x+1)/ 7 =…

Q: 4 B A 6 -$ -4 -3 -2 2 3 4 5 -1 -2 -3 -4 -5 1. Identify the center of rotation and give the…

A: for canter of rotation we join the adjacent point of two triangles which located in first and second…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A:

Q: Find the parametric equations for the line passing through points P(2, -3, 1) and Q(4, 1, -4)

A: Given points are  P2,-3,1,Q4,1,-4

Q: 10 4 2 E -8 -4 -2 4 6. 8. -2 2.

A: rotation 270 degrees counterclockwise around the origin is (x,y) changes to (y, -x)

Q: A carnival ride is drawn on a coordinate plane so that the first car is located at the point (30,…

A:

Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

A:

Q: When the 2-dimensional shape shown below is rotated about the axis indicated by the dashed line, a…

A: Given shape: A triangle

Q: Part 1 of A trench must be dug from point B, straight to point A (which is at the southern point of…

A: Let's find coordinates of A.

Q: Find the parametric equations of the line L2 that passes through the point P(-9, 1, -6) and is…

A: Given that the line L2 passes through the point -9,1,-6 and is parallel to the line given parametric…

Q: 278. Find symmetric equations of the line passing through point P(2, 5, 4) that is perpendicular to…

A: Topic = Vector As per guidelines , At a time only question can be answered. please repost for other…

Q: 13. Given the points A(3,5) and B( – 3, – 7), find b. the parametric equations of the line.

A:

Q: 7. Evaluate [4y-xds where C is the upper portion of the circle centered at the origin of radius 3…

A: To Evaluate: ∫C(4y-x)ds, where C is the curve represented in the given figure.

Q: 277. Find parametric equations of the line passing through point P(-2, 1, 3) that is perpendicular…

A:

Q: 9. 8- 3-12-11-10 -9 -8-7-6-5 3-2-1, -2- -3- -6- -7- -8- -9- Write the parametric equation for the…

A: