Let P, Q, and R be the points at 1 on the x-axis, 2 on the y-axis, and 3 on the z-axis, respectively. Find QP x QŘ.

Q: Sketch the set of points (r, 0) that satisfy the following conditions: {(r, 0) : –2 <r < 2, –7/4 < 0…

A: Polar curve sketch

Q: Verify that the following pairs of curves meet orthogonally. a. x2 + y2 = 4,   x2 = 3y2  b. x = 1 -…

A: Given:Verify that the following pairs of curves meet orthogonally.

Q: Let C C R? be the path from (3, –2) to (3, 2) along the graph of the curve x – 5x?y? – 7x2 = 0.…

A:

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A:

Q: Find the max. and min. values of (x, y) = x² – xy + y on the quarter circle x² +y =1 where x.y20.

A: I use langrange multiplier method

Q: Find the point (a, b) on the graph of y = ex where the value ab is theleast.

A:

Q: Which of the following planes contains the z-axis?x + y = 1

A:

Q: Suppose (p o) is the point on the graph of V closest to (1, 0) - What is the value of p+O? y=Vx 3…

A: Basic derivative problem

Q: Points X and Y are respectively 12 m north and 5 m east of point Z. Calculate XY.

A: To solve this problem we use the Pythagorean theorem

Q: Find the condition for the points (a, 0). (h, k){0,b) when ab = 0 to be collinear.

A: Find the condition for the given points to be collinear.

Q: F· dr, where F(x,y) = –lj, and C is the part of the graph of y = - x from (2,2) to (–2, C

A:

Q: Find a plane containing the point (6, -4,-3) and the line (t) = +t 270

A:

Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

A:

Q: Find an equation for the set of points in an xy-plane that are equidistant from the point P and the…

A: Find the equation for the set of points in an xy-plane that are equidistant from the point P -6,3…

Q: Find the shortest distance, d, from the point (5, 0, -8) to the plane x + y + z = 8. d =

A:

Q: If 1x, y2 are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

A: If (x,y) are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

Q: If f(x,y,z) = x2 + y2, what is the locus of points in space for which grad f is parallel to the…

A:

Q: Find the locus of the points P(x, y) such that PA = 2PB where A is the point with coordinates (0, 3)…

A:

Q: Describe with a sketch the sets of points 1x, y, z2 satisfying the following equations. y - z = 0

A: First sketch the graph of the function y-z=0 as shown below.

Q: Show that the condition that the curves ax²+by²=1 a'x?+b'y²=1 1 1 1 1 Should intersect orthogonally…

A: If m1 = tangent at point (x,y) and     m2 = tangent at point (x,y) then Orthogonal conditions is…

Q: Find the locus of the points that are equidistant to the point F(0,2) and the line y =-2. A) y? = 4x…

A: We can find the answer as given below

Q: Find a path c(t) that traces the line y = 2x + 1 from (1, 3) to (3, 7) for 0 ≤ t ≤ 1.

A: Given:

Q: find the distance d between the points P1 and P2. P1 = (1.2, 2.3); P2 = ( - 0.3, 1.1)

A: The question is taken from the Analytical Geometry in which we have to find the distance between the…

Q: find the point p such that v=pq has the components (5,-7,-4)

A: find the point p such that v=pq has the components (5,-7,-4)

Q: If the distance from P(1, 0) to the point T(12) is x, determine the coordinates P(1,0) of the point…

A: Find coordinates

Q: 7. If 1x, y2 are the coordinates of a point P in the xy-plane,then x is called the__________________…

A: Given that, x,y are the coordinates of a point P in the xy-plane. The objective is to fill in the…

Q: O Find an equation for the plane through the point P = (3, −2, 4) that is perpendicular to the line…

A: Given problem:- Find an equation for the plane through the point P = (3, -2, 4) that is…

Q: Draw a set of x-, y-, and z-axes and plot the following points: с. С(0, 0, —3) d. D(2, 3, 0) a. A(1,…

A: The graph is shown in next step.

Q: Find the exact length of the curve. y = In(1 - x²), o s x s

A: Solve the problem using definite integral

Q: Evaluate ||x'y dA if D is the triangle in the xy-plane with vertices at (0,0), (5,2), and (0,2).

A:

Q: Find t for the following terminal points: (a) P(0, 1), t = (0) P(-, ), t =| (c) P(-1,0), t = (d)…

A:

Q: Find the number  a such that the line x = a  bisects thearea under the curve  y = 1 / x 2  , 1&lt;…

A: Our Aim is to find a number such that line x=a bisects the area under the curve y=1x2, 1≤x≤4.

Q: Find the coordinates of the reflection without using the coordinate plane. P (4,6) over the x-axis.

A:

Q: Find the relation between x and y such that the point (x,y) is equidistant from the points (7,1) and…

A:

Q: Find the condition for the points(a, 0).(h, k)(0, b) when ab 0 to be collinear.

A: When points are colllinear area should be 0Therefore, 12a01hk10b1=012ak1b1+1hkb1=0

Q: Find i x w if ||T|| = 3, ||w|| = 4, 0 = and ī, w both lie in the xz-plane (as shown). 3 %3D

A:

Q: Q1) Find the locus of the points that are equidistant to the point F(0,2) and the line y = -2. A) y²…

A:

Q: Find the value of x if H is the midpoint of GJ , GJ = 4x – 6, and GH = 27. 14. %3D

A: We have to calculate the value of x

Q: Find the cоттоn points of the circles (x + 1)² + (y – 1)² = 5 and x² + y? = 1.

A: Common points of the circles simply means the point of intersection of the given circles.

Q: Find the points on the curve y-9x closest to the point (0, 4). ) and (O

A:

Q: 12. Let v =|0 and y For what value(s) of h is y in the plane -3 -2 generated by v and v2?

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

Q: In a plane, l lm and t 1 m. l and t related? By appearance, how are

A: We know that in a plane if l⊥m and t⊥m then l will be parallel to t So, l and t are related as l∥t

Q: Let Q = 4x? + 6xy+ 4y². The points on the curve Q = 7 which are closest to the origin are:

A:

Q: Find the point at which the line 7(t) +t intersects the | xz plane.

A:

Q: Determine all points P(x,y) such that PA = PB. A = (2,3) and B is on the line y=-3

A: solution:- A(2,3) B(0,-3)

Q: If C1 is the segment connecting (x1, Y1) to (x2, Y2), find | x dy – y dx in terms of the four…

A:

Q: If B is the midpoint of AC, with point A at (5, 2) and point C at (9, 0), what is the equation of…

A:

Q: Prove that three points (x1, yl), (x2, y2) and (x3, y3) are collinear ( on the same straight line)…

A:

Q: Draw a set of x-, y-, and z-axes and plot the following points: с. С(0, 0, —3) d. D(2, 3, 0) e. Е(2.…

A: Solve by making graph

Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.