The sum of two vectors is the largest when the two vectors are _____.

Asked by maham237 @ 28/11/2020 in Mathematics viewed by 388 People

Answered by maham237 @ 28/11/2020

The sum of two vectors is largest when both vectors are parallel and share the same direction.

Further explanation

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.

$C^2 = A^2 + B^2 - 2 \cdot A \cdot B \cdot cos(\pi + \theta)$

Where $\theta$ is the angle between the 2 initial vectors. From the above equation we can see that C will be maximum when the cosine of $\pi + \theta$ will be minimum, this happens when both vectors are parallel and share the same direction ( $\theta$ would be zero and $cos(\pi + \theta) = -1$ ).

As further knowledge, C will be minimum when the cosine of $\pi + \theta$ will be maximum, this happens when both vectors are parallel but have opposite direction ( $\theta$ would be equal to $\pi$ and $cos(\pi + \theta) = 1$ ).

Learn more

Cosine theorem: brainly.com/question/1621839
How to add vectors: brainly.com/question/10841907

Keywords

Cosine theorem, addition of vectors, maximum

The sum of two vectors is the largest when the two vectors are _____.

Further explanation

Learn more

Keywords

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