The sum of two vectors A and B is maximum when both vectors are :
A)parallel
B) opposite in direction
C) perpendicular to each other
D) A inclined 45 with B
E) none of the above
A)parallel
a. Parallel
To determine which option results in the maximum sum of vectors A and B, we need to consider the concept of vector addition. Vector addition is a geometric operation where vectors are added together to obtain a resultant vector.
In this case, we want to maximize the sum of vectors A and B. Let's analyze each given option and its effect on vector addition:
A) Parallel Vectors: When two vectors are parallel, their sum will be the maximum. This is because the vectors' magnitudes add up directly and result in a larger resultant vector.
B) Opposite Direction Vectors: When two vectors are in opposite directions, their sum will be the minimum. This is because the vectors will partially cancel each other out, resulting in a smaller resultant vector.
C) Perpendicular Vectors: When two vectors are perpendicular (at a 90-degree angle), their sum will not be the maximum. The magnitude of the resultant vector will be the square root of the sum of the squared magnitudes of vectors A and B. Thus, the maximum sum is not achieved when the vectors are perpendicular.
D) Inclined at 45 Degrees: When two vectors are inclined at an angle of 45 degrees, their sum will not be the maximum either. The maximum sum occurs when vectors are parallel, as mentioned in option A.
Therefore, the correct answer is A) parallel.