
The length of the projection of the line segment joining the points (5, -1, 4) and (4, -1, 3) on the plane is
Answer
507.3k+ views
2 likes
Hint: First of all, we will find the angle between the plane and the line joining the given two points, using the formula given as follows:
Where, is the angle between the plane and line, are direction ratios of a line and are direction ratios of plane. A clear figure will be helpful. Then, we can make use of the formula for projection as
Complete step-by-step answer:
We have been asked, to find the projection of the line segment joining the point (5, -1, 4) and (4, -1, 3) on the plane
We know that, direction ratio of a is equal to the difference of their respective coordinates.
Direction ratio of line joining points A and B is given by,
direction ratio of the line.
Now, the equation of the plane is therefore, the direction ratio of the plane is (1, 1, 1)
Using the formula,
Here, we have, .Therefore, substituting these in the above formula, we get,
Multiplying the numerator and denominator with 2, we get,
Cancelling similar terms, we get,
Using the distance formula between the two points i.e.
We can clearly see that, the projection of the line segment AB on the plane is equal to
Using, we get,
Therefore, the correct option is A.
Note: The diagram is very important in this question, as it will help you to think how to proceed further, to get the required result.
Be careful while finding the projection because sometimes we just miss the square root over 2 and choose the answer as which is wrong.
Where,
Complete step-by-step answer:
We have been asked, to find the projection of the line segment joining the point (5, -1, 4) and (4, -1, 3) on the plane

We know that, direction ratio of a is equal to the difference of their respective coordinates.
Direction ratio of line joining points A and B is given by,
Now, the equation of the plane is
Using the formula,
Here, we have,
Multiplying the numerator and denominator with 2, we get,
Cancelling similar terms, we get,
Using the distance formula between the two points i.e.
We can clearly see that, the projection of the line segment AB on the plane is equal to
Using,
Therefore, the correct option is A.
Note: The diagram is very important in this question, as it will help you to think how to proceed further, to get the required result.
Be careful while finding the projection because sometimes we just miss the square root over 2 and choose the answer as
Latest Vedantu courses for you
Grade 9 | CBSE | SCHOOL | English
Vedantu 9 CBSE Pro Course - (2025-26)
School Full course for CBSE students
₹37,300 per year
EMI starts from ₹3,108.34 per month
Recently Updated Pages
Master Class 9 General Knowledge: Engaging Questions & Answers for Success

Master Class 9 English: Engaging Questions & Answers for Success

Master Class 9 Science: Engaging Questions & Answers for Success

Master Class 9 Social Science: Engaging Questions & Answers for Success

Master Class 9 Maths: Engaging Questions & Answers for Success

Class 9 Question and Answer - Your Ultimate Solutions Guide

Trending doubts
Give 10 examples of unisexual and bisexual flowers

Draw a labelled sketch of the human eye class 12 physics CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Differentiate between insitu conservation and exsitu class 12 biology CBSE

What are the major means of transport Explain each class 12 social science CBSE

Why is the cell called the structural and functional class 12 biology CBSE
