4. What are the coordinates of point A? (0.0,5) (0,6 (0,6,0 Flgure 1 O (2, 0, 5)

Q: 3. The plane in ' with equation 4x=34 %3D

A:

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: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: 5. The ends of the transverse axis are at (+8,0) and the ends of the conjugate axis are at (0. 16).

A:

Q: 3. Sketch the points determined by the following. (a) Iz+1-i = 2 %3D (b) Im(2z +i) +1=0

A:

Q: A,B,C are three points on OX ,OY ,OZ respectively at distance a,b,c (a'0,b'0,c'0)from the origin…

A:

Q: Find the angle between the planes 2x + y- 3z 2 and -x + 2y - z= 1.

A: We can solve the given problem as follows:

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,,n2, n2),B(m,,m2,m3),C(r,,r2, 13).

A: Please see the explanation below

Q: 2. Find the exact value of the distance between the line of intersection of the planes 2x - y + 2z =…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 1. Find the distance from the point S(2,-3,4) to the plane x+2y+ 2z =13

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Determine the location of a point (x, y, z) that satisfies the condition  ∣y∣ ≤ 3

A: If ∣y∣ ≤ 3 the point lies with in 3 units from xz plane on left side if y < 3 , or within 3 units…

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: Calculate the distance between the points L= (8, 0) and K= (1, –4) in the coordinate plane. Give an…

A:

Q: The plane through the point (3,-1,2) can perpendicular to the a) x-axis b) y-axis c) z-axis d) non d…

A:

Q: y -6- 4- 3- 2- 1- -3 2 -1 0 12 3 4 5 6 -1- -2- R -3- your work on question 10, classify this…

A:

Q: y U(a, b) V(?, ?) h =b units T(0, 0) a units W(c, 0)

A: HL congruence postulate: According to this congruence postulate, two right triangles are congruent…

Q: 7. Find the distance between the point (3, 1, –2) and the plane x + 2y – 2z = 4.

A: Given that plane x+2y-2z=4 and point 3,1,-2To find :Distance between point and plane Solution if…

Q: The midpoint of AB is M(2, –2). If the coordinates of A are (-2, 1), what are the coordinates of B?

A: Recall: Mid point Formula: The midpoint of M(x,y) of the line segment from A(x1,y1) to B(x2,y2) is…

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

A:

Q: (b) Let A(4,4, 7) and B(11,8, 11) be two points in 3D. Determine the coordinates of the point Q…

A: Introduction: When a vector is a non-zero scalar multiple of another vector, the two vectors are…

Q: 4 and the plane Find the point on the curve of intersection of the paraboloid x- + y- x - y + 2z = 0…

A:

Q: Determine the location of a point (x, y, z) that satisfies the condition z = −5

A: The condition is z = −5

Q: 10. The distance between the point (3,-2,5) and the plane 2x+2y+z=5 is NONE

A: Given: The distance between (3,-2,5) and the plane 2x+2y+z=5

Q: with the guldin's proposition 1 get the contents of the rotating object that occurs if the land…

A: As per the question we are given a 2d region bounded by the curve : y = 6 - 3x - x2 and the straight…

Q: A plane can be determined by points, that are not on the same line. OA. unable to be determined OB.…

A:

Q: find distance between plane(6x_2y_z+4=0)and point (3,2,1) P 3:08

A: Given,           The plane is 6x-2y-x+4=0 and the point is 3,2,1.

Q: 5) Find the distances by drawing the figures and right triangle used to calculate a. Between 1₁ =…

A: Given: Let's determine the distance for the following, a) medium of l1=2+2t,-1+t,-3t and…

Q: 5. Calculate the distance between the point (3, 1, -2) and the plane 2x + y-2+1. O 10 o -10 V14 O 10…

A: The equation of the plane is  2x+y-z+1 = 0 The point is x0,y0,z0 =3,1,-2 To evaluate : The distance…

Q: 1. Find the distance from the center of the sphere given by (x-2)² +(y+2)²+(z-1)² = 4 to the point…

A: Given equation of the sphereis x-22+y+22+z-12=4So center of the sphere be 2,-2,1and the given…

Q: Through one of the two intersection points of two circles, a diameter in each of the circles is…

A:

Q: 3. Determine the angle between the planes: x - z+7=0 2x +y-z+8 = 0

A:

Q: 4. Triangle PQR has sides defined by [x, y] = [1, -3] + t [0, 1], [x, y] = [2, 4] + m [-1, -6], and…

A: 1. For finding the length of the sides of the given triangle, we need to find the coordinates of…

Q: d the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10

A:

Q: 5. Find the coordinates of the point P(2,4) with respect to the translated axis with origin at…

A:

Q: 2. Find the coordinates of the y-intercept of the plane (x, y, z)=(4,6,5) +s(2,3,1) + t(3,6,12)

A: To find out the coordinate of y-intercept.

Q: 5. What are the coordinates of the centroid of triangle FGH: F(6,-1), G(12,4), H(15,-2)?

A: follow next step

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

A: We will use direct formula to find the angle. The detailed solution is as follows below:

Q: 2. The midpoint of AB is M(4,2). If the coordinates of A are (6,-4), what are the coordinates of B?…

A: Since, we have been given that the midpoint of AB is M(4,2) and coordinates of A(6,-4). Then Our Aim…

Q: Calculate the distance between the points G = (-3, 3) and E = (5, -2) in the coordinate plane. Give…

A:

Q: *15. What is the name for the point on the coordinate plane that has the (Inv. 7) coordinates (0,…

A: The given point is: (0, 0)

Q: Given four points A(2, 3, 5), B(6,9, 15), C(0,0, 5), D(-2, –3, 10) in 3D Cartesian coordinates, we…

A: We are given four points on the 3D Cartesian coordinates with the image plane as z=2 And we have to…

Q: 8. If the vertices of a triangle are A(8, 5), B(-1, 8) and C(2, -1) where would the centroid (Center…

A: Consider the vertices of a triangle is (x, y). The vertices of a triangle are: A(8, 5), B(-1, 8) and…

Q: Use Green's Theorem to evaluate $4x²ydx+2ydy where C is the triangle with vertices (0,0), (1,2), and…

A:

Q: Find the points on the plane r - y = 2 – z closest to the point (1, 1, 1).

A: We will find the closest point on the given plane as following.

Q: The diagram shows AB graphed on a coordinate plane. B (4, 6) 6- -5 4 3 2 -5 -4 -3 -2 -1 4 -1- -2 3…

A:

Q: 8. What is the angle between the two planes x+y=0 and y-z=2?

A:

Q: The distance from (10,-9,5) to yZ-plane is - 10 B.9 OC.5 OD. 206 OE. /106

A: We will find the distance between the point and the yz plane as following.

Q: Consider the points P = (3, 2, 1) and Q = (1, 2, 3) in R3. (1) What is the equation of the sphere…

A: Answer

Q: 16. Triangle CDE with vertices C(2, 4), D(6, 7), and E(7, 3): 90° counterclockwise about the origin

A: New points after rotation 90 degree counter clock wise about the origin is given by: X = xcosθ +…