Answered: r, m and n be the direction cosines of…

Math

Geometry

r, m and n be the direction cosines of the line L. Show that r2 + m2 + n2 = 1.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

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

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

Chapter10: Analytic Geometry

Section10.CR: Review Exercises

Problem 38CR

See similar textbooks

Related questions

Q: Verify that the two lines are parallel and find the distance between the lines. L1: x = 2 − t, y…

Q: Let l,,l2,lz be the lines X(t) = (1,1, 2) + t(1,2,3), X(s)= (9,8,11) + s(2,1,1) and X (r) = (0,0,0)…

Q: Let I be the line (1, -1, 1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l. distance

Q: Find a and b such that the lines r1 = (1, 2, 1) + t(1, −1, 1)andr2 = (3, −1, 1) + t(a, b, −2) are…

A: Given: r1=1,2,1+t1,-1,1 r2=3,-1,1+ta,b,-2 r1 and r2are parallel only if a1=b-1=-21

Q: MO and PR are parallel lines.

Q: Show that the line joining the points P(0,1,2) and Q(3,4,8) is parallel to the line joining the…

Q: Let A= (1,2,4), B=(4,1,5), C=(4,2, 6), D=(7,1,7) Find the exact distance between the lines AB and…

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

Q: Lines ℓ and m are intersected by transversal t and ℓ ∥ m. If m∠3 = 126°, what is m∠5?

A: The pairs of angles on one side of the transversal but inside the two lines are called Consecutive…

Q: Determine whether the lines r1(t) = 〈0, 1, 1〉+ t〈1, 1, 2〉 and r2(s) = 〈2, 0, 3〉+ s〈1, 4,…

A: line1:xyzt1+t1+2t and line2:xyz2+s4s3+4sto find the point of intersection we need to equate both the…

Q: Prove that given lines are skew. L1: [x, y, z] = [1, 3, 7] + t[–1, 1, 2] L2: [x, y, z] = [4, –2,…

Q: al to the line given as :

A: Which of the following planes is normal to the line given as: x=2t+3, y=5t-7 , z=t-4

Q: Determine whether the lines L1 and L2 passing through the pairs of points are parallel,…

A: Slope is basically the vertical or the horizontal change between two distinct points. In a graph,…

Q: Determine whether the lines h and I, intersect, are parallel, or are skew. 1: n= 4i+3j+ (i-j+6k) 12:…

Q: 3. Show that the lines L1 : x = 2+t, y= 2+3t, z = 3+t and L2:1 = 2+t, y= 3+ 4t, z = 4 + 2t…

A: L1: x =2+t , y= 2+3t , z= 3+t L2: x =2+t , y= 3+4t , z= 3+t

Q: Show that the lines whose direction cosines are given by l+m+n=0,2mn+3nl-5lm=0 are perpendicular to…

Q: Show that the lines whose direction cosines are given by 1+m+n=0 ,2mn+3ln- 5lm=0 are perpendicular…

A: The given direction cosines arel+m+n=02mn+3ln-5lm=0

Q: Construct a line perpendicular to the line given through the point P at the right.

A: To plot the line perpendicular to the given line through the point P

Q: For the points P,(-5,2,1) and P2(3,4,0), find the direction of P,P2 and the midpoint of line segment…

A: Solve the given

Q: Determine the point of intersection of the lines γ1 : ¯r1(t) = ⟨3, 2, 1⟩ + t⟨1, 0, 1⟩ and γ2 :…

A: First let's suppose both line are intersecting each other so, r1 = r2 then solve for t and s.

Q: If A, B, C and C`are constants, show that: (a) the lines: Ах + By + C%3 0 Ах + By + C' 3 0 are…

Q: 3. Show that the lines L :1 = 2+t, y = 2+3t, 2 = 3+t and La :1 = 2+t, y = 3+ 4t, 2 = 4+ 2t…

Q: Find the value of a that makes lines u and v parallel. 125 + x x+65 O -5 O 12

A: Solution

Q: find the distance between the Linel L) through A(I,0,-1), B (-1,)andthe Line (L2) through C…

Q: Determine whether the lines L1: (0, −1), (5, 9) and L2: (0, 3), (4, 1) passing through the pairs of…

A: Given: Line L1 passes through 0, -1 and 5, 9.Line L2 passes through 0, 3 and 4, 1 To Find: To…

Q: Suppose that two lines Re((1+i)z+2i+3) = 0 and Re(2-bi)z+5) perpendicular. then b=. 0 are ||

A: We will convert the equation into cartesian form and then use condition for perpendicular lines

Q: Determine whether the lines L1: (−2, −1) and L2: (1, 3), (5, −5) passing through the pairs of points…

A: Since, we have been given that two lines are L1: (-2,-1), (1,5) and L2: (1,3) , (5,-5). Our Aim is…

Q: Which of the lines x – y + 3 = 0 and x – 4y –7= 0 is father from the origin? -

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

Q: Suppose L, is the line through the origin in the direction of u and L2 is the line through the point…

A: We are given two lines L1 and L2 in 3d, and we have to find the closest points x1 , x2 such that the…

Q: Determine B such that the line 3x + 2y - 7 = 0 is perpendicular to 2х - Ву+23D0. | O 5 Оз O 2

Q: Consider points A, B, C, and D, no three of which are collin- ear. Using two points at a time (such…

A: Given information: A, B, C and D are four points in which no three points are collinear.…

Q: E. Show that the lines 3x - 5y + 19 =0 and 10x + 6y -50 =10 are perpendicular and find their point…

Q: Which of the following denotes the length of a line segment with endpoints A and B?

A: Answer: B) AB¯

Q: Determine if the lines ℓ1: x − 9 = −t, y + 4 = 3t, z − 9 = 3t and ℓ2: x − 1 = s, y − 4 = −s, z − 9…

Q: D F OF and GI are parallel lines and mZDEH = 116°, %3D Submit

A: DF and GI are parallel line,

Q: 12- Show that the lines L1 and L2 are parallel and also find the distance between them. L1: x=2-t,…

A: Solution: Consider the given lines in parametric form; L1:Consider x = 2 - t = x0+ aty = 2t = y0 +…

Q: Determine whether the lines 2x + 5y =7 and 5x +2y =2 are perpendicular true or false

A: Compare the equations with standard equation y=mx+c

Q: Show that the lines whose direction cosines are given by 1+m+n=0 ,2mn+3ln-5lm=0 are perpendicular to…

A: Our objective is to show two lines whose direction cosines given are perpendicular.

Q: Find the point of intersection of the lines r;(t) = (-1, 1) + t(8, 4) and rɔ(s) = (2, 1) + s(8, 6)…

A: Consider the given lines in polar form. To find the intersection points equate the x and y…

Q: If the point (4, 1) is the midpoint of the line PD , where P (x, 3), D (7, y) , find the value…

Q: Find b so that the points (4,-6), (5,-8), and (b,-2) lie on the line

A: Please find the solution in the attached images :

Q: For the line €: (x, y, z) = (2, 3, 4) + n(3, - 2, 5), find a) a point of the line. b) a direction…

A: the given line is: l:x,y,z=2,3,4+n3,-2,5 we have to find: (a) a point of the line. (b) a direction…

Q: Is the line that contains the points P1(−3, 1) and P2(1, 3) perpendicular to the line that…

A: We can check the line joining the points are perpendicular or not as per the concepts as below.

Q: Show that the lines px + qy + r = 0 and P1x + q1y +r¡ = 0 are parallel or identical if and only if…

Q: Let I be the line (1, -1, 1) + t(0, 2, 1). Let Q = (1,0, 1). Find the distance from Q to l.

A: In a 3 dimensional space, a point and a line can be at infinite number of distance from each other,…

Q: Prove that the lines r = (1, 2, −1) + t(2, 2, 1) and r = (−1, −2, 3) + s(4, 6, −3) intersect, and…

Q: Determine whether or not the line through the points A(0, –4, 2) and B(5, –1, 0) is perpendicular to…

Question

Let r, m and n be the direction cosines of the line L. Show that r² + m² + n² = 1.

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

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Graphs$

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.

Similar questions

Prove that if two lines neither horizontal nor vertical are perpendicular, then the product of their slopes is -1. HINT: See Figure 10.19. You need to show and use the fact that ABC~EDC.
For the line l:x,y,z=2,3,4+n3,-2,5, find a a point of the line. b a direction vector for the line.
Does the relation is perpendicular to have a reflexive property consider line l? A symmetric property consider lines l and m? A transitive property consider lines l, m and n?
Use drawings, as needed, to answer each question. Does the relation is parallel to have a areflexive property? consider a line m bsymmetric property? consider lines m and n in a plane ctransitive property? consider coplanar lines m, n, and q
Draw and describe the locus of points in the plane that are equidistant from parallel lines l and m. _________________________________________ ________________________________________
Given: A line m and a point T not on m Suppose that you do the following: i Construct a perpendicular line r from T to line m. ii Construct a line s perpendicular to line r at point T. What is the relationship between lines s and m?
The point mid ay between (a, b) and (c, d) _____________. So the point midway between (1, 2) and (7, 10) is ___________.