Class 11 Exam > Class 11 Questions > The addition of vectors and the multiplicatio...
Start Learning for Free
The addition of vectors and the multiplication of a vector by a scalar together gives rise to
- a)commutative law
- b)asymmetric laws
- c)distributive laws
- d)intransitive law
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The addition of vectors and the multiplication of a vector by a scalar...
Explanation:
If a vector is multiplied by a scalar as in pA→ , then the magnitude of the resulting vector is equal to the product of p and the magnitude of A→, and its direction is the same as A→ if p is positive and opposite to A→ if p is negative.
Distributive law for scalar multiplication:
p(A→ +B→ )=pA→ +pB→
Most Upvoted Answer
The addition of vectors and the multiplication of a vector by a scalar...
Distributive Law in Vectors
The distributive law is one of the fundamental laws of algebra. It states that the multiplication of a number (scalar) with a sum of two or more numbers (vectors) is equal to the sum of the scalar multiples of each individual number (vector).
For example, if we have two vectors A and B, and a scalar k, then the distributive law states that:
k(A + B) = kA + kB
Similarly, if we have three vectors A, B, and C, and a scalar k, then the distributive law states that:
k(A + B + C) = kA + kB + kC
Importance of Distributive Law in Vectors
In the context of vectors, the distributive law is important because it allows us to simplify calculations involving vector addition and scalar multiplication. Using the distributive law, we can factor out a common scalar multiple from a sum of vectors, which can make calculations much easier.
For example, suppose we have two vectors A and B, and we want to compute the vector 3A - 2B. Using the distributive law, we can write:
3A - 2B = 3A + (-2)B
= 3A + (-1)(2B)
= 3A + (-1)(2)B
= 3A + (-2)B
= 3A - 2B
Therefore, we can see that the distributive law allows us to simplify the expression 3A - 2B by factoring out the common scalar multiple -2.
Conclusion
In summary, the addition of vectors and the multiplication of a vector by a scalar together give rise to the distributive law, which is a fundamental law of algebra that allows us to simplify calculations involving vector addition and scalar multiplication. This law is important in many areas of mathematics and physics, and is essential for understanding the properties of vectors.
The distributive law is one of the fundamental laws of algebra. It states that the multiplication of a number (scalar) with a sum of two or more numbers (vectors) is equal to the sum of the scalar multiples of each individual number (vector).
For example, if we have two vectors A and B, and a scalar k, then the distributive law states that:
k(A + B) = kA + kB
Similarly, if we have three vectors A, B, and C, and a scalar k, then the distributive law states that:
k(A + B + C) = kA + kB + kC
Importance of Distributive Law in Vectors
In the context of vectors, the distributive law is important because it allows us to simplify calculations involving vector addition and scalar multiplication. Using the distributive law, we can factor out a common scalar multiple from a sum of vectors, which can make calculations much easier.
For example, suppose we have two vectors A and B, and we want to compute the vector 3A - 2B. Using the distributive law, we can write:
3A - 2B = 3A + (-2)B
= 3A + (-1)(2B)
= 3A + (-1)(2)B
= 3A + (-2)B
= 3A - 2B
Therefore, we can see that the distributive law allows us to simplify the expression 3A - 2B by factoring out the common scalar multiple -2.
Conclusion
In summary, the addition of vectors and the multiplication of a vector by a scalar together give rise to the distributive law, which is a fundamental law of algebra that allows us to simplify calculations involving vector addition and scalar multiplication. This law is important in many areas of mathematics and physics, and is essential for understanding the properties of vectors.
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
|
|
Similar Class 11 Doubts
Top Courses for Class 11View all
The addition of vectors and the multiplication of a vector by a scalar together gives rise toa)commutative lawb)asymmetric lawsc)distributive lawsd)intransitive lawCorrect answer is option 'C'. Can you explain this answer?
Question Description
The addition of vectors and the multiplication of a vector by a scalar together gives rise toa)commutative lawb)asymmetric lawsc)distributive lawsd)intransitive lawCorrect answer is option 'C'. Can you explain this answer? 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 addition of vectors and the multiplication of a vector by a scalar together gives rise toa)commutative lawb)asymmetric lawsc)distributive lawsd)intransitive lawCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The addition of vectors and the multiplication of a vector by a scalar together gives rise toa)commutative lawb)asymmetric lawsc)distributive lawsd)intransitive lawCorrect answer is option 'C'. Can you explain this answer?.
The addition of vectors and the multiplication of a vector by a scalar together gives rise toa)commutative lawb)asymmetric lawsc)distributive lawsd)intransitive lawCorrect answer is option 'C'. Can you explain this answer? 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 addition of vectors and the multiplication of a vector by a scalar together gives rise toa)commutative lawb)asymmetric lawsc)distributive lawsd)intransitive lawCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The addition of vectors and the multiplication of a vector by a scalar together gives rise toa)commutative lawb)asymmetric lawsc)distributive lawsd)intransitive lawCorrect answer is option 'C'. Can you explain this answer?.
Solutions for The addition of vectors and the multiplication of a vector by a scalar together gives rise toa)commutative lawb)asymmetric lawsc)distributive lawsd)intransitive lawCorrect answer is option 'C'. Can you explain this answer? 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 addition of vectors and the multiplication of a vector by a scalar together gives rise toa)commutative lawb)asymmetric lawsc)distributive lawsd)intransitive lawCorrect answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The addition of vectors and the multiplication of a vector by a scalar together gives rise toa)commutative lawb)asymmetric lawsc)distributive lawsd)intransitive lawCorrect answer is option 'C'. Can you explain this answer?, a detailed solution for The addition of vectors and the multiplication of a vector by a scalar together gives rise toa)commutative lawb)asymmetric lawsc)distributive lawsd)intransitive lawCorrect answer is option 'C'. Can you explain this answer? has been provided alongside types of The addition of vectors and the multiplication of a vector by a scalar together gives rise toa)commutative lawb)asymmetric lawsc)distributive lawsd)intransitive lawCorrect answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The addition of vectors and the multiplication of a vector by a scalar together gives rise toa)commutative lawb)asymmetric lawsc)distributive lawsd)intransitive lawCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice Class 11 tests.
|
|
Explore Courses for Class 11 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup