The sum of two vectors is the largest when the two vectors are _____.
Asked by maham237 @ in Mathematics viewed by 395 People
Asked by maham237 @ in Mathematics viewed by 395 People
Answered by maham237 @
The sum of two vectors is largest when both vectors are parallel and share the same direction.
When adding two vectors, the result will always be a new vector which depends on 3 things, the modulus of the two initial vectors and the angle between them . Given two random vectors, their sum will be largest when the modulus of the result will be maximum.
Suppose we start with 2 random vectors of modulus A and B. The modulus of their sum, let's call it C, will be expressed by the cosine theorem.
Where is the angle between the 2 initial vectors. From the above equation we can see that C will be maximum when the cosine of will be minimum, this happens when both vectors are parallel and share the same direction ( would be zero and ).
As further knowledge, C will be minimum when the cosine of will be maximum, this happens when both vectors are parallel but have opposite direction ( would be equal to and ).
Cosine theorem, addition of vectors, maximum
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