The vector sum of two forces is perpendicular to their vector differences. In that case the forces
- are equal to each other
- are equal to each other in magnitude
- are not equal to each other in magnitude
- cannot be predicted
The Correct Option is B
Solution and Explanation
$\Rightarrow A ^{2}-\vec{ A } . \vec{ B }+\vec{ B }. \vec{ A }- B ^{2}=0$
$\Rightarrow A = B$
$(\because \vec{ A }. \vec{ B }=\vec{ B }. \vec{ A })$
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Concepts Used:
Addition of Vectors
A physical quantity, represented both in magnitude and direction can be called a vector.
For the supplemental purposes of these vectors, there are two laws that are as follows;
- Triangle law of vector addition
- Parallelogram law of vector addition
Properties of Vector Addition:
- Commutative in nature -
It means that if we have any two vectors a and b, then for them
\(\overrightarrow{a}+\overrightarrow{b}=\overrightarrow{b}+\overrightarrow{a}\)
- Associative in nature -
It means that if we have any three vectors namely a, b and c.
\((\overrightarrow{a}+\overrightarrow{b})+\overrightarrow{c}=\overrightarrow{a}+(\overrightarrow{b}+\overrightarrow{c})\)
- The Additive identity is another name for a zero vector in vector addition.
Read More: Addition of Vectors