Among the given magnitudes, which magnitude is not possible when a vector of magnitude 3 is added to a vector of magnitude 4? Is it 7, 0, 1 or 5?
Vectors are very interesting and important concepts that have many applications in engineering and physics. Many problems regarding kinematics and projectile motion can be solved using these concepts.
Answer: Among the given values, the magnitude is not possible when a vector of magnitude 3 is added to a vector of magnitude 4, is 0.
Let's get into the explanation of the solution.
Since the magnitudes of the vectors are given, we can have any of the three cases given below.
- The vectors are in the same direction: When the vectors are in the same direction, their magnitudes are added. If both these vectors are in x-direction, then 3î + 4î = 7î. Hence, 7 is not the answer.
- The vectors are in the opposite direction: When the vectors are in the opposite directions, their magnitudes are added. If the vector of magnitude 3 is in x-direction and the other is in x-direction, then 3î - 4î = -î. Hence, the magnitude is 1. Hence, it is not the answer.
- The vectors are perpendicular to each other: Now, if the vectors are in the perpendicular direction then the resultant is found by using Pythagoras theorem. If the vectors are in x and y directions respectively, the √(32 + 42) = 5. So, 5 is also not the answer.
From the above cases, we can see that neither of 7, 1 or 5 is the answer. Hence, the answer to the given question is zero.
This can be explained as the minimum resultant value of two vectors are when they are opposite to each other (180 degrees angle), which is 1. Hence, the resultant can't be zero.