2. If you were to rotate ABCD 90° counterclockwise about the origin, what would the coordinate of A' be? B 5 4. 3 1. -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4 O a) (-5, 5) J)(-5, 3) Ob) (-3, 5) O d) (-3, 3)

Q: Chapter 13, Section 13.6, Question 033 Find Vz. z = sin (8y – 4xy) Give your answer in unit vector…

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Q: 1 Suppose a line passes through the point (1, 1 and parallel to the 2' 3 plane x + y + z = 0. Then…

A: The direction vector of the normal to the plane is (1,1,1) Given that the line is parallel to the…

Q: Calculate the distance from point A(1, 2, 1) to the plane of equation 3x-4y + 5z = 1.

A: To find distance of point to plane using the formulae: Given point is and plane equation is .

Q: The image of (-2 , 5) under reflection y = -x followed by translation with translation vector (-3 ,…

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Q: Calculate gij for the distance between (x;) = (1, 1, – 1) and (yi) = (0,1,2) in %3D T-2 1] barred…

A: A point in three dimensional coordinate system is given by xi=1,1,-1yi=0,1,2 Now the point in barred…

Q: The distance from (9,-6, 7) to yZ-plane is A9 O B. 6 OC. 166 OD. 85 O E.7

A: Distance of a point (a,b,c) from yz plane is as In yz plane x coordinate is zero and y= b and z= c.…

Q: Find a parametrization for the line segment beginning at P,(4, - 7,- 7) and ending at P2(0, - 7,2).

A: The line segment beginning at P1<4, -7, -7> and ending at P2<0, -7, 2>

Q: 6. Determine the distance from the point (2, -1, 5) to the plane 3x - 3y + 5z = 8.

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Q: Find a vector equation for the line segment that joins P(1,3,4) to Q(-2,4,6)

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Q: Find the point(s) on the plane 4x +3y +z = 2 that are closest to (1,-1,1).

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Q: Find the angle between the vectors (9, -2) and (-8, -3). Carry your intermediate computations to at…

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Q: 4. Find the angle made between the two planes: r+ y - z = 5 and 2r + y +3z = -1.

A: Given that: Equation of first plane: x+y-z=5   ........(1)Equation of 2nd plane: 2x+y+3z=-1…

Q: if vector AB=i+7j-4k and B is the point (9,3,5) find A

A: Let A=ai^+bj^+ck^B=di^+ej^+fk^ be twovectors.Then AB→=d-ai^+e-bj^+l-ck^

Q: 2. Determine the angle, to the nearest degree, between the vectors * = (4,6,-2) and y = (1,8,2)

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Q: what is the vector equation of the line of intersection of the planes z=5 and x=9

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Q: The line that passes through the point (4, –2, 0) and parallel to the vector (1, 2, –3) has…

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Q: What are the new coordinates of point M (-8, 3) after a rotation 180° counterclockwise? • (8, -3) •…

A: We find new point after 180 degree rotation counterclockwise.

Q: Suppose a line is given parametrically by the equation L (t) = (2 -t.t-1, -t-2). Then the vector and…

A: Given:    Parametric equation L(t) = (2 - t , t - 1, - t - 2)    The line containing the point (x0,…

Q: Find the angle between the vectors (5, -3) and (-9, -8). Carry your intermediate computations to at…

A: Using formula of Angle between two vectors.

Q: You need to guide a robot from the red dot on the left to the green dot on the right, avoiding the…

A: The solution is as below

Q: If vector A A→ has unity magnitude and makes an angle of 60 degrees with the +x axis, then the x and…

A: Solution:

Q: 8. Find the angles between the planes r+y = 1, 2x+ y – 2z = 2

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Q: The line that passes through the point (4, -2,0) and parallel to the vector (1, 2, –3) has symmetric…

A: The solution is given in the next step.

Q: 3. Give the parametric and symmetric equations of the line that passes through he point (4, –3, 5)…

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Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Here, the given equation of the plane is 3x+y-6z=8 So, the coefficients of x,y and z will give us…

Q: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

A: Given, A line segment passes through the points P1,-1,2 and Q4,1,7 We have, the vector equation of a…

Q: Suppose L(5, 4) was reflected across the line y = x then translated along the vector . What is the…

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Q: Let vector AB = (2,3,1). If the coordinates of A are (2,1,5), what are the coordinates of the point…

A: Vector AB= B-A

Q: Suppose a line is given parametrically by the equation L (t) = (1- 3t,3t – 4, -3-t)- Then the vector…

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Q: Compute the angle between the two planes 2x + 3y + 7z = 2 and 4x - 2y + 2z = 4.

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Q: 9. Find the angle between the two planes 2x + 3y + z = 3 and x + 3y + 2z = -3

A: Given,           2x+3y+z=3    and   x+3y+2z=-3We know that,           Suppose the two equation be…

Q: The vector parallel to intersection line of the two planes 4x-y+z=2 and 2x+y- 2z=3 is: *

A: Plan 1: 4x-y+z=2 Plan 2: 2x+y+2z=3

Q: Find the angle between the vectors (4, 2) and (7, -2). Carry your intermediate computations to at…

A: solve the following

Q: Find the equation for the plane through the point Po = (2,10,7) and normal to the vector n = 9i + 2j…

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Q: Find the angle between the vectors (2, 1) and (3, -2) to the neareast second.

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Q: Find the distance of point 4(2-/3,2) from the line that passes through the origin and parallel to…

A: Distance of a point A(x1, y1) from the line ax+by+c=0 is given by d=ax1+by1+ca2+b2

Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

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Q: Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z.…

A: The equation of a line that passes through the point x0 , y0 , z0 in three dimensional space is…

Q: Find the point on the plane 2x + 2y + 5z = 2 that is closest to the point P(- 3, 5, – 5). (x, y, z)…

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Q: Chapter 13, Section 13.6, Question 033 Find Vz. z = sin (4y² – 5xy) Give your answer in unit vector…

A:

Q: Find the distance from S(1, 1, 3) to the plane 3x + 2y + 6z = 6.

A: It is given that a point S1, 1, 3 and the equation of the plane 3x+2y+6z=6   Here x1=1, y1=1, z1=3…

Q: Which of the following is the equation with center (-9, 8) Major axis = 10? %3D 20 and minor axis…

A: To find the equation of the vertical ellipse with center (-9,8) . Major axis = 20 and minor axis =…

Q: find the equation of the line through (0,2,1) that is perpendicular to both u= 4i + 3j − 5k and the…

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Q: The vector (1, 0, 0) makes a 45 degrees with the vector (x, y, z). What is the relationship between…

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Q: What will be the new coordinates of point M (-5, -7) after a rotation of 270° counterclockwise about…

A: To fins the new coordinate of point M (-5,-7) after a rotation of 270° anticlockwise about the…

Q: Find the distance from the point (5, 4, 3) to the plane −4x−1y−1z=4.

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Q: The plane containing the point (-4,1,3) and parallel to the plane 4x + 7y – 3z = 2 has equation Ar +…

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Q: Find the distance from the point (1, -2, 4) to the given plane 3x + 2y + 6z = 5 Thank you.

A: To find the distance from the point (1, -2, 4) to the given plane 3x + 2y + 6z = 5

Q: The equation of plane through (3,-1,7) and perpendicular to the vector (4,2,-5) is 4x + 2y5z-25 = 0.…

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Q: John is standing at point (1, 0) on a gigantic circular track of radius 1 mile with center (0, 0).…

A: Given query is to find the measure of the angle.