Indicate whether the statement is true or false. 1. There is only one scalar equation for a given line in 3-space. 2. A line in 3-space can be represented by using a scalar equation, a vector equation, parametric equations. 3. Three collinear points in space will define a plane. 4. [0,2,1] +t[2,1,1] is parallel to the plane 2x+y+z=0 5. If the normal vectors of three planes in 3-space are coplanar then there is no solution to the system

Indicate whether the statement is true or false. 1. There is only one scalar equation for a given line in 3-space. 2. A line in 3-space can be represented by using a scalar equation, a vector equation, parametric equations. 3. Three collinear points in space will define a plane. 4. [0,2,1] +t[2,1,1] is parallel to the plane 2x+y+z=0 5. If the normal vectors of three planes in 3-space are coplanar then there is no solution to the system

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

See similar textbooks

Related questions

Q: 6. [8.5] Consider the points A(1, 3, 1), B (2, 1, 0), and C(5, 1, 1). Determine the Cartesian…

Q: Find a scalar equation of the plane x + 2y + 3z = 0 -x+ 3y - 2z = 0 c. 13x + y - 5z = 9 d. 13x+y- 5z…

Q: d an equation for the plane that passes through the origin and is perpendicular to the line (t) =…

Q: Based on the points A(5,6,7), B(6,7,12), C(7,12,5). Write the equation of your plane in Vector,…

A: Step 1:Three points are…

Q: 13 Given: m4CXE = mZFZH mZ1 = mZ3 Prove: m2 = mZ4 Statement Reason 1 M2CXE = mZ1+ m2 Reason ? 2…

A: Given: m∠CXE=m∠FZHm∠1=m∠3 We have to prove that m∠2=m∠4 Statement 1: m∠CXE=m∠1+m∠2 Reason for 1: The…

Q: Find an equation for the plane containing the three points (0, 1, -1), (1,0,1), and (2, 1, 0). Where…

Q: Find the equation of the plane parallel to the line r = 2i + t(−4i + 3j + 8k) and containing the…

Q: A particle moves at constant speed 1445 units along the curve of intersection of the two the two…

Q: 17. Explain why it is not possible for a line in three-space to be represented by a scalar equation…

Q: 2. Consider the plane determined by the three points (3,−1, 2), (8, 2, 4) and (−1, −2, —3). (a) Find…

A: Given: Three Points P=(3,-1,2),Q=(8,2,4) and R=(-1,-2,-3) PQ = <5, 3, 2> PR = <-4, -1,…

Q: Which of the following equations define the plane passing through the points (3,0, 0), (0, –7,0),…

Q: 7. Find the scalar equation of any plane which contains the line = (1,2,1)+ t(3,6,-1)

Q: 5. A line is defined by the parametric equations x = -2 – t, and y = 4+ 2t, te R (a) Does the point…

Q: 3. A plane contains A(1, -3, 2), B(-2, 4, 2) and C(3, 2, 1). (a) Determine the vector equation of…

Q: Consider the line passing through the points (2, -3,4) and (5,10, -12). Describe the line by a.…

Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

Question

Indicate whether the statement is true or false.
1. There is only one scalar equation for a given line in 3-space.
2. A line in 3-space can be represented by using a scalar equation, a vector equation,
parametric equations.
3. Three collinear points in space will define a plane.
4. [0,2,1] +t[2,1,1] is parallel to the plane 2x+y+z=0
5. If the normal vectors of three planes in 3-space are coplanar then there is no solution to
the system

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 with 2 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

Can you do part 4 and 5

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

5. Let W be a plane that satisfies (a) Describe the plane in vector form, explaining your reasoning step by step. (b) Describe the plane in normal form, explaining your reasoning. (c) Pick two values of b and let W₁ and W₂ be the corresponding planes. Discuss how the two planes are different and similar. 3(x-1)+2(y+3)+2(z-2) = b, where b is a real number.
Find an equation for the plane containing the two (parallel) lines v (0, 1, -4) + t(1, 3, -5) and v, = (4, –1, 0) + t(1, 3, –5). %3D
3 4 33. Determine the vector equation, parametric equations, and, if possible, symmetric equation of the line that passes through the point P(1, 3, 5) and a. has direction vector (-2, -4, -10) b. also passes through the point Q(-7, 9, 3) c. is parallel to the line that passes through R(4, 8, -5) and S(-2, -5,9) d. is parallel to the .x-axis e. is perpendicular to the line (x, y, z) = (1, 0, 5) + (-3, 4, -6) f. is perpendicular to the plane determined by the points A(4, 2, 1), 4 2), and C(-3, 2, 1) nd 59 nsv of -3 of the plane that
Q1 Find an equation for the plane through the points (−4,−2,0),(−6,−6,2) and (−7,0,−4). Enter your answer in general or scalar form.(refer the image to screenshot) And Also find the distance between the point (0,−4,1) and the above plane. d=