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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?
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→
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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.
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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 2025 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 2025 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 2025 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 2025 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?.
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