Class 11 Exam  >  Class 11 Questions  >  The magnitude of resultant of P vector and q ... Start Learning for Free
The magnitude of resultant of P vector and q vector is r. if q vector and p vector is increased by 3 times and two times respectively then resultant is increased root by 6 times . find the relation between q vector and p vector.?
Most Upvoted Answer
The magnitude of resultant of P vector and q vector is r. if q vector ...
Given:
The magnitude of the resultant of vector P and vector Q is r.

Let's assume:
Let the initial magnitude of vector P be P and the initial magnitude of vector Q be Q.

Step 1: Determine the initial magnitude of the resultant:
The magnitude of the resultant vector is given as r. We can represent the magnitude of the resultant vector as:

|r| = √(Px^2 + Qx^2)

Where Px and Qx represent the initial magnitudes of vectors P and Q respectively.

Step 2: Determine the new magnitudes of vector P and vector Q:
According to the problem, vector Q is increased by 3 times and vector P is increased by 2 times. Therefore, the new magnitudes of vector P and vector Q become:

New magnitude of vector P = 2P
New magnitude of vector Q = 3Q

Step 3: Determine the new magnitude of the resultant:
According to the problem, the resultant is increased by √6 times. Therefore, the new magnitude of the resultant vector becomes:

|new r| = √6 * |r| = √6 * √(Px^2 + Qx^2)

Step 4: Determine the relation between vector P and vector Q:
To find the relation between vector P and vector Q, we need to compare the initial and new magnitudes of the resultant vector.

|new r| = √(4P^2 + 9Q^2)

Since |new r| = √6 * √(Px^2 + Qx^2), we can equate the two equations:

√6 * √(Px^2 + Qx^2) = √(4P^2 + 9Q^2)

Squaring both sides:

6(Px^2 + Qx^2) = 4P^2 + 9Q^2

Simplifying:

6Px^2 + 6Qx^2 = 4P^2 + 9Q^2

Rearranging:

2P^2 - 6Px^2 = 3Q^2 - 6Qx^2

Dividing both sides by 2:

P^2 - 3Px^2 = (3/2)(Q^2 - 2Qx^2)

Conclusion:
The relation between vector P and vector Q is that the difference between P^2 and 3Px^2 is equal to three halves of the difference between Q^2 and 2Qx^2.
Attention Class 11 Students!
To make sure you are not studying endlessly, EduRev has designed Class 11 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 11.
Explore Courses for Class 11 exam

Top Courses for Class 11

The magnitude of resultant of P vector and q vector is r. if q vector and p vector is increased by 3 times and two times respectively then resultant is increased root by 6 times . find the relation between q vector and p vector.?
Question Description
The magnitude of resultant of P vector and q vector is r. if q vector and p vector is increased by 3 times and two times respectively then resultant is increased root by 6 times . find the relation between q vector and p vector.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about The magnitude of resultant of P vector and q vector is r. if q vector and p vector is increased by 3 times and two times respectively then resultant is increased root by 6 times . find the relation between q vector and p vector.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The magnitude of resultant of P vector and q vector is r. if q vector and p vector is increased by 3 times and two times respectively then resultant is increased root by 6 times . find the relation between q vector and p vector.?.
Solutions for The magnitude of resultant of P vector and q vector is r. if q vector and p vector is increased by 3 times and two times respectively then resultant is increased root by 6 times . find the relation between q vector and p vector.? in English & in Hindi are available as part of our courses for Class 11. Download more important topics, notes, lectures and mock test series for Class 11 Exam by signing up for free.
Here you can find the meaning of The magnitude of resultant of P vector and q vector is r. if q vector and p vector is increased by 3 times and two times respectively then resultant is increased root by 6 times . find the relation between q vector and p vector.? defined & explained in the simplest way possible. Besides giving the explanation of The magnitude of resultant of P vector and q vector is r. if q vector and p vector is increased by 3 times and two times respectively then resultant is increased root by 6 times . find the relation between q vector and p vector.?, a detailed solution for The magnitude of resultant of P vector and q vector is r. if q vector and p vector is increased by 3 times and two times respectively then resultant is increased root by 6 times . find the relation between q vector and p vector.? has been provided alongside types of The magnitude of resultant of P vector and q vector is r. if q vector and p vector is increased by 3 times and two times respectively then resultant is increased root by 6 times . find the relation between q vector and p vector.? theory, EduRev gives you an ample number of questions to practice The magnitude of resultant of P vector and q vector is r. if q vector and p vector is increased by 3 times and two times respectively then resultant is increased root by 6 times . find the relation between q vector and p vector.? tests, examples and also practice Class 11 tests.
Explore Courses for Class 11 exam

Top Courses for Class 11

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev