The sum of 2 vectors is the smallest when the angle between them is :
a) 0
b) 45
c) 90
d) 180
d) i believe is the correct answer but i'm not sure exactly. Thanks in advance for your help.
correct
You are correct, the sum of two vectors is the smallest when the angle between them is 180 degrees (or straight opposite). This is because when the vectors are aligned opposite to each other, they cancel out each other's magnitudes, resulting in a smaller overall sum. Hence, the correct answer is d) 180.
To find the angle between two vectors that gives the smallest sum, you need to consider the concept of vector addition using the parallelogram law.
Let's break it down step by step:
1. Start by considering two vectors, let's call them A and B.
2. The sum of two vectors is given by the vector addition, which is obtained by placing one vector's tail at the head of the other vector.
3. Now, draw the parallelogram with the two vectors as adjacent sides.
4. The diagonal of the parallelogram represents the vector sum, which is the smallest when the vectors are aligned in the same direction, or in other words, when the angle between them is 0 degrees. This occurs when the vectors are collinear, resulting in the smallest possible sum.
Therefore, the correct answer is a) 0.