the sum of vectors with the Pythagorean theorem allows us to find that the maximum magnitude occurs for the case:
d) the two vectors are parallel
Vectors are physical quantities that have modulus and direction, for example: force, velocity, acceleration, etc.
Vector algebra has defined the sum, the product by a scalar and by a vector. The modulus and the direction of the resulting vector must be encoded.
The sum of two quantities is done using the Pythagorean theorem
c² = a² + b²
where c is the resultant called hypotenuse, a and b are the summing vectors called legs; trigonometry is used for the direction.
Let's apply this expression to the present case
a, b) perpendicular vectors
c² = a² + b²
c =
c = 11.7
the magnitude is the same in both cases, changing the direction of the vector
c) Antiparallel vectors
For this case the vectors are collinear, so the sum reduces to the algebraic addition
c = a-b
c = 6 -10
c = -4
d) parallel vectors
c = a + b
c = 4 + 10
c = 14
We can see that the vectors addition gives their maximum and minimum values when the vectors are collinear.
In conclusion using the vectors addition we find that the correct answer is
d) the two vectors are parallel
learn more about vector addition here: