Respuesta :
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.
[tex]C^2 = A^2 + B^2 - 2 \cdot A \cdot B \cdot cos(\pi + \theta)[/tex]
Where [tex]\theta[/tex] is the angle between the 2 initial vectors. From the above equation we can see that C will be maximum when the cosine of [tex]\pi + \theta[/tex] will be minimum, this happens when both vectors are parallel and share the same direction ([tex]\theta[/tex] would be zero and [tex]cos(\pi + \theta) = -1[/tex]).
As further knowledge, C will be minimum when the cosine of [tex]\pi + \theta[/tex] will be maximum, this happens when both vectors are parallel but have opposite direction ([tex]\theta[/tex] would be equal to [tex]\pi[/tex] and [tex]cos(\pi + \theta) = 1[/tex]).
Learn more
- Cosine theorem: https://brainly.com/question/1621839
- How to add vectors: https://brainly.com/question/10841907
Keywords
Cosine theorem, addition of vectors, maximum
The sum of two vectors is the largest when the two vectors are “in the same direction”.
Further explanation:
Explanation:
The physical quantities have two types’ scalar and vector.
Those physical quantities that have only magnitude are known as scalar quantities.
Those physical quantities that have magnitude and direction are known as vector quantities.
Force, velocity, weight are vector quantities. They have both direction and magnitude.
The resultant sum of the two vectors can be obtained by the formula given below.
[tex]R = \sqrt {{A^2} + {B^2} + 2AB\cos \theta }[/tex]
The maximum value of the resultant is at [tex]{0^ \circ }[/tex] and the minimum value of the resultant is at [tex]{180^ \circ }.[/tex]
[tex]\boxed{\cos {0^ \circ } = 1{\text{ and cos18}}{{\text{0}}^ \circ } = - 1}[/tex]
If the two vectors are in the same direction then the angles between them is [tex]{0^ \circ }[/tex] and the sum of the vectors is largest.
If the two vectors are in opposite direction then the angles between them is [tex]{180^ \circ }[/tex] and the sum of the vectors is smallest.
The sum of two vectors is the largest when the two vectors are “in the same direction”.
Learn more:
- If the clothing maker bought 500 m2 of this fabric, how much money did he lose? use 1tepiz=0.625dollar and 0.9144m=1yard https://brainly.com/question/2479097.
- Suppose that you find the volume of all the oceans to be 1.4×109km3 in a reference book. to find the mass, you can use the density of water, also found in this reference book, but first you must convert the volume to cubic meters. what is this volume in cubic meters? https://brainly.com/question/1446243.
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Vectors
Keywords: sum of vectors, largest sum, to vectors, same directions, parallelogram law of vector addition, vector addition, acceleration, seconds, x component, y component, velocity, t = 0, function, function of time t.
