UrbanPro
Login Ask & Answer Success Stories Paid Courses Free Classes Tuition & Classes Fees Write a Review All Categories Help Center
Post your Learning Need Signup as a Tutor
✕

Popular Cities

Bangalore

Hyderabad

Delhi

Mumbai

Chennai

Pune

Kolkata

Gurgaon

Ahmedabad

Jaipur

Noida

✕

Take Class I-V Tuition from the Best Tutors

  • Affordable fees
  • 1-1 or Group class
  • Flexible Timings
  • Verified Tutors

Book a Free Demo

Class I-V Tuition > Learn Class I-V Tuition > If l,m,n be three real numbers proportional to the...
✕

Search in

If l,m,n be three real numbers proportional to the direction cosines of a line L.then l²+m²+n²=1

Asked by Last Modified  

11 Answers

Learn Class I-V Tuition

Follow 0
Answer

Please enter your answer

Genuine artist in teaching mathematics in a very very simple yet exciting way

If a, b, c are three numbers proportional to the direction cosine l, m, n of a straight line, then a, b, c are called its direction ratios. They are also called direction numbers or direction components. Hence by definition, we have 1/a = m/b = n/c = k (say) => l=ak, m=bk, n=ck => k2(a2...
read more
If a, b, c are three numbers proportional to the direction cosine l, m, n of a straight line, then a, b, c are called its direction ratios. They are also called direction numbers or direction components. Hence by definition, we have 1/a = m/b = n/c = k (say) => l=ak, m=bk, n=ck => k2(a2 + b2 + c2) = l2 + m2 + n2=1 => k = ± 1 / ?a2 + b2 + c2 = ± 1/??a2 l = ± a/??a2. Similarly m = ± b/??a2 and n = ± n/??a2 where the same sign either positive or negative is to be chosen throughout. Example: If 2, – 3, 6 be the direction ratios, then the actual direction cosines are 2/7, –3/7, 6/7. Note: Direction cosines of a line are unique but direction ratios of a line in no way unique but can be infinite. read less
Comments
Dislike Bookmark

1541252

yes true
Comments
Dislike Bookmark

Target learning

yups true.
Comments
Dislike Bookmark

Tutor

yes
Comments
Dislike Bookmark

Free Mathematics Teaching and Guidance to Very Weak Students in study

YES
Comments
Dislike Bookmark

Tutor

yes
Comments
Dislike Bookmark

Badminton player

yes
Comments
Dislike Bookmark

Tutor

Direction cosines can be written in terms of direction ratios. l = a/sqrt(a^2+b^2+c^2), m = b/sqrt(a^2+b^2+c^2) n = c/sqrt(a^2+b^2+c^2) So, l^2+m^2+n^2 = (a^2+b^2+c^2)/(a^2+b^2+c^2) =1
Comments
Dislike Bookmark

Tutor

If l , m and n are the direction cosines of any line, then l² + m² + n² = 1 Proof: Let OP be drawn through the origin parallel to the given line so that l , m , n are the cosines of the angles which OP makes with OX, OY and OZ respectively. Let (x, y , z) be the co-ordinates of any point P on this...
read more
If l , m and n are the direction cosines of any line, then l² + m² + n² = 1 Proof: Let OP be drawn through the origin parallel to the given line so that l , m , n are the cosines of the angles which OP makes with OX, OY and OZ respectively. Let (x, y , z) be the co-ordinates of any point P on this line. Let OP = r , then x = lr , y = mr , z = nr Squaring and adding , we obtain x² + y² + z² = ( l² + m² + n²) r² l² + m² + n² = (x² + y² + z²) / r² but r² = OP² =(x² + y² + z²) Thus l² + m² + n² = 1 Proved. read less
Comments
Dislike Bookmark

English teacher with 5 years of experience in teaching,• Instructed students in English language arts, including writing, reading comprehension, speaking, listening and understanding

RELATION BETWEEN DIRECTION COSINES: If l , m and n are the direction cosines of any line, then l² + m² + n² = 1 Proof: Let OP be drawn through the origin parallel to the given line so that l , m , n are the cosines of the angles which OP makes with OX, OY and OZ respectively. Let (x, y , z) be the...
read more
RELATION BETWEEN DIRECTION COSINES: If l , m and n are the direction cosines of any line, then l² + m² + n² = 1 Proof: Let OP be drawn through the origin parallel to the given line so that l , m , n are the cosines of the angles which OP makes with OX, OY and OZ respectively. Let (x, y , z) be the co-ordinates of any point P on this line. Let OP = r , then x = lr , y = mr , z = nr Squaring and adding , we obtain x² + y² + z² = ( l² + m² + n²) r² l² + m² + n² = (x² + y² + z²) / r² but r² = OP² =(x² + y² + z²) Thus l² + m² + n² = 1 Proved. read less
Comments
Dislike Bookmark

View 9 more Answers

Related Questions

What is the name of the jelly-like substance that is inside the cell? A: cytoplasm B: ectoplasm C: cytokinesis
A.cytoplasm
Puneet Kr. Mishra
water(h2o) is? 1-compound 2-mixture 3-eliment 4-mineral
1.compound
Shailesh
What is Soil erosion?
Soil erosion is the washing or blowing away (by water or wind) of the top layer of soil .
Rayyan
Addition of 12 and 11
When you add 12 and 11, the answer you get is 23. Method: 12 + 11 = 23.
Bilal
What are the parts of integumentary system?
The integumentary system consists of the skin, hair, and nails all performing essential functions for the body
Nagamani

Now ask question in any of the 1000+ Categories, and get Answers from Tutors and Trainers on UrbanPro.com

Ask a Question

Related Lessons

Zeitadverbien....Time Adverbs

Priyankush

0 0
0
Geradeaus, Rechts, Links ...Wohin gehen Sie ? {Where are you going ? { Straight, right, left } }

Priyankush

0 0
0
Je...., desto..... . ( The...... , the......)

Priyankush

1 0
0
वृद्धि संधि उदाहरण
अद्य + एव = अद्यैवलता + एव = लतैवतथा + एव = तथैवसदा + एव = सदैव देव + ऐश्‍वर्यम् = देवैश्‍वर्यम्आत्‍म + ऐक्‍यम् = आत्‍मैक्‍यम् अ/आ + ओ/औ = औ जल + ओघ: = जलौघ:मम + ओषधि: = ममौषधि:नव...

Arun

2 0
0
Mixed Numbers and Improper Fractions
A mixed number is a combination of a whole number and a fraction. For example, if you have two whole apples and one half apple, you could describe this as 2 + 1/2 apples, or 21/2 apples. Writing...
A

Amrtha S.

0 0
0

Recommended Articles

5 Qualities Of a Good Teacher That Can Win...

Well, teachers are considered to be the shaper of society. They stand in a very high position not just because of their job role but for an underlying sense of respect that has been associated with the profession since ancient times. The most exciting thing about this profession is that a good teacher can help the students...

Read full article >

6 Different Types of History

Many believe that history is a subject to study the past. To some extent, it is true but broadly, speaking history is a lot more than that. This subject lets us know about the glorious historical events that took place and make us proud of them. Besides, it also alerts us about our mistakes, the lessons we learned from...

Read full article >

Does your Child need a Tutor?

A tutor can be a real guide for a child and help him/her prosper academically and personally. However before you get down to the imperative question of - Does your child needs a tutor... you need to understand the significance of what exactly a tutor can do for your child. A tutor is a teacher who guides the student in...

Read full article >

Can You Imagine Life Without Mathematician?

Mathematics is one of the most important subjects students need to learn to have a great career ahead and solve many mathematical problems we come across every day. Mathematics is a popular subject because of its utility in every aspect of life. Without maths, leading an everyday and functional life is nearly impossible....

Read full article >

Find Fourth standard near you
Fourth standard in Delhi
Fourth standard in Bangalore
Fourth standard in Hyderabad
Fourth standard in Kolkata
Fourth standard in Mumbai
Fourth standard in Chennai
Fourth standard in Pune
Fourth standard in Lucknow
Fourth standard in Noida
Fourth standard in Ghaziabad

Looking for Class I-V Tuition ?

Learn from the Best Tutors on UrbanPro

Are you a Tutor or Training Institute?

Join UrbanPro Today to find students near you
X

Looking for Class I-V Tuition Classes?

The best tutors for Class I-V Tuition Classes are on UrbanPro

  • Select the best Tutor
  • Book & Attend a Free Demo
  • Pay and start Learning

Take Class I-V Tuition with the Best Tutors

The best Tutors for Class I-V Tuition Classes are on UrbanPro

This website uses cookies

We use cookies to improve user experience. Choose what cookies you allow us to use. You can read more about our Cookie Policy in our Privacy Policy

Accept All
Decline All

UrbanPro.com is India's largest network of most trusted tutors and institutes. Over 55 lakh students rely on UrbanPro.com, to fulfill their learning requirements across 1,000+ categories. Using UrbanPro.com, parents, and students can compare multiple Tutors and Institutes and choose the one that best suits their requirements. More than 7.5 lakh verified Tutors and Institutes are helping millions of students every day and growing their tutoring business on UrbanPro.com. Whether you are looking for a tutor to learn mathematics, a German language trainer to brush up your German language skills or an institute to upgrade your IT skills, we have got the best selection of Tutors and Training Institutes for you. Read more

ThinkVidya Learning Pvt Ltd © 2010-2024All Rights Reserved