Solve Q4c, d & e with detailed explanations 4. The planes 1 and 1, are have cartesian equations x – y + z +1 = 0 and 2x + y – z – 1 = 0respectively.a) Show that these two planes are not parallel.b) Find a parametric equation of their line of intersection.c) Give a Cartesian equation of plane 13 passing through point A(1, –1,–1) and perpendicularto π and πρ.Given the points B(2,3, – 1) and C(4, –1,5),d) Evaluate OC.OBe) Show that OB^OC can be expressed in the form m(0A), where m is a scalar. Give ageometrical interpretation of your results.

* As per our guidelines, we are supposed to solve only the first three problems/subdivisions. Please…

4. The planes , and 12 are have cartesian equations x – y+ z+1 = 0 and 2x + y – z – 1 = 0 respectively. a) Show that these two planes are not parallel. b) Find a parametric equation of their line of intersection. c) Give a Cartesian equation of plane t3 passing through point A(1, –1,–1) and perpendicular to π, and π, Given the points B(2,3, – 1) and C(4, –1,5), d) Evaluate OC.OB e) Show that OB^oċ can be expressed in the form m(OẢ), where m is a scalar. Give a geometrical interpretation of your results.

4. The planes , and 12 are have cartesian equations x – y+ z+1 = 0 and 2x + y – z – 1 = 0 respectively. a) Show that these two planes are not parallel. b) Find a parametric equation of their line of intersection. c) Give a Cartesian equation of plane t3 passing through point A(1, –1,–1) and perpendicular to π, and π, Given the points B(2,3, – 1) and C(4, –1,5), d) Evaluate OC.OB e) Show that OB^oċ can be expressed in the form m(OẢ), where m is a scalar. Give a geometrical interpretation of your results.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.3: Hyperbolas

Problem 36E

See similar textbooks

Related questions

Q: 4. The planes 1 and 1, are have cartesian equations x – y + z +1 = 0 and 2x + y – z – 1 = 0…

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

Q: Find the Cartesian equation of the plane containing the point P(1,3,-2) and the I T = (0, -1, 4) +…

Q: Consider the hyperboliode H defined by the equation: x^2+y^2−z^2=1 and the point P0=(1,4,4) in H.…

A: We are given the following hyperboloid : x2 + y2 - z2 = 1 And we have to choose the correct…

Q: Determine the point on the plane 2x + 3y − 4z = 0 that is closest to the point P(1, 1, 1)

Q: 1. The planes defined by the equations x + 2y – 2z = 3 and 2x + 4y - 4z = 7 are parallel. Find a…

Q: Let a be the plane containing the line Sy-z-2=0 | 2x + z = 0 and the point (0, 1,0). Which of the…

A: Plane- surface problem....

Q: Example 7: Determine whether the planes x- 3y + 6z = 4 and 5x+ y - z = 4 are orthogonal, parallel,…

Q: Question 4: A plane parallel to y-axis passing through line of intersection of planes x + y + z = 1…

A: A plane parallel to y-axis passing through line of intersection of planes x + y + z = 1 and 2x + 3y…

Q: What is the parametric equation for the line of intersection of the planes x + y - z = 2 and 3x - 4y…

Q: (a) Prove that the lines with parametric equations: x = 1+t, y = 1+ 6t, z = 2t and x = 1+ 2s, y = 5…

A: aLet the L1 be the line:x=1+t, y=1+6t,z=2tand L2 be the line:x=1+2s, y=5+15s, z=-2+6sThe direction…

Q: Find parametric equation of the line joining points P{(2,4, –1) and P2(5,0, 7). Where does it…

A: To do this we need the vector V→ that will be parallel to the line. This can be any vector as long…

Q: In three space, find the parametric equations of the curve C of intersection of the cylinder S: a +…

Q: Determine the general equation of the plane 2 passing through the point P(1, –4, –5) and parallel to…

Q: a) Show that the shortest distance between the point (a, b, c) and the plane Ax + By + Cz + D = 0 is…

A: Part(a): Given, The point is a,b,c And, the plane is, Ax+By+cZ+D=0

Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1: 2x –…

A: Line of intersection

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

A: Solution

Q: find the equation of the plane with the given description. Passes through O and is parallel to 4x −…

A: Solution:Given A plane 4x − 9y + z = 3To find the equation of the plane passess through O and is…

Q: . Given the point Q(1,-2,4) and a plane p: 3x + 2y + 6z = 5, find a) The distance from Q to p. b)…

Q: Find the point Q symmetric to the point P (1; 3; —4) with respect to the plane 3x+y-2z=0

Q: Find the point p(x, y, z) on the plane 2x + y - z - 5 = 0 that is closest to the origin.

A: Given:The given plane is 2x+y-z-5=0 that is closest to the origin.To find:we have to find…

Q: Q1) the plane has equation of 4x-3y-2+5=0 Pud equation of plane partlel to R) and contimons with…

A: Given that: Equation of given plane is: 4x-3y-245=0and contains point (2,1,3)

Q: Find the equation of the plane that contains point P(1, -1, 2) and has the normol n= 2¿+3j+Sk.

Q: Given: a plane containing the point P(-2, 5, -3) and the line [x, y, z] = [-1,2,5] + s[3, –4,1]…

Q: Find a parametric representation of the line through the point P(3,1,-4) and perpendicular to the…

Q: Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0)…

A: Given equation of plane ax+by+cz+d=0. The plane ax+by+cz+d=0 will divide the xyz space into two…

Q: The part of the plane 2x 5y + z = 10 that lies above the triangle with vertices (0, 0), (0, 6), and…

A: Double integration need to be done.

Q: At which point will the plane 2x + 4y – 3z = -48 and the line given by the parametric equations x =…

Q: 6) Consider the plane P : x+y – z = 0 in R³ that contains both the points P(1,0, 1) and P2(0, 1, 1).…

A: • In the first part, we have to use the general Cartesian equation of a line passing through two…

Q: Consider the plane P :r+y-z=0 in R that contains both the points P:(1,0,1) and P:(0, 1, 1). Answer…

A: The equation of the straight line passing through 2 points is , , . Here, the points are .

Q: 1. Let C, be the line segment from the origin to (3, 2, 0); C2 be the shorter circular arc of the…

A: Note: According to Bartleby we have to solve the first three subparts please upload the question…

Q: 1. Find the equations of the planes that are exactly 4 units from the plane 2x-2y+z=6

Q: 9) Find a parameterization of the line formed by the intersection of the following planes: P,: 2x –…

A: Cross product of normals of planes is normal to the required line of intersection

Q: Example 6: Determine whether the planes 3x+ y- 4z = 3 and -9x-3y+12z= 4 are | orthogonal, parallel,…

Q: Which of the following are parametric equations of the line of intersection of the planes x+2 z=3,…

A: We have to check

Q: ). Find a parametric representation for the line of intersection of the following two planes: I - y…

A: We use cross product to find the direct vector for the line.

Q: 4 /5 . 135% + - (a) Find parametric equations for the line of intersection of the planes x+2y- = 3…

A: In X plane, put y=z=0 & in Y plane put x=z=0 &in Z plane put x=y=0

Q: The line in R³ through the point Po(xo, Yo, zo) and parallel to the vector v = parametric equations…

A: Given that the position vector of the point is P0 (x0, y0, z0) and parallel to the vector v = (v1,…

Q: 6) Consider the plane P: z+y-2:= 0 in R³ that contains the point P₁(1, 1, 1). Answer the following…

A: As per the question we are given the plane P and a point P1 on it. Now we have to find the…

Q: Compute the parametric equations of the line in R3 determined by the intersection of the two planes:…

A: To obtain the parametric equations of the intersection line, use the following formulae. Let n1→…

Q: The part of the plane 3x + 2y +: - 6 that lies in the first octant

Q: 02. A. Show that the plane 3x + y - z = 9 and the line {x = 2,y = -1+ 3t ,z = 1+ 3t} are parallel,…

Q: Find the point on the plane 3x + 2y + z = 6 that is nearest the origin.

Q: Find a plane that contains S and is perpendicular to the plane that contains the points

Q: Verify that the line r(t) = [1 + t, 1 - t, t] is part of the one sheeted hyperboloid x^2 + y^2 -…

Q: 9) Find a parameterization of the line formed by the intersection of the following planes: P,: 2x -…

Q: Find the equation of a plane containing Po (1, 2, 3) and perpendicular to n = .

A: We have to find the equation of a plane containing P0 (1,2,3) and perpendicular to n = <1, -1,…

Q: a) Prove that the lines with parametric equations: x = 1+ t, y = 1 + 6t, z = 2t and x = 1+ 2s, y = 5…

A: Given that: Line L1: x=1+t, y=1+6t, z=2tLine L2: x=1+2s, y=5+15s, z=-2+6s

Q: 2. Find a parameterization of the line formed by the intersection of the following planes: P1: 2x –…

A: 2)as per our guideline we have to write one question at a time kindly repost remaining questions

Question

Solve Q4c, d & e with detailed explanations

4. The planes 1 and 1, are have cartesian equations x – y + z +1 = 0 and 2x + y – z – 1 = 0
respectively.
a) Show that these two planes are not parallel.
b) Find a parametric equation of their line of intersection.
c) Give a Cartesian equation of plane 13 passing through point A(1, –1,–1) and perpendicular
to π and πρ.
Given the points B(2,3, – 1) and C(4, –1,5),
d) Evaluate OC.OB
e) Show that OB^OC can be expressed in the form m(0A), where m is a scalar. Give a
geometrical interpretation of your results.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Pyramids$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage