A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum might be…?
A vector with a magnitude of 20 is added to a vector with a magnitude of 25. What could be the magnitude of the resulting vector?
(a) 12
(b) 50
(c) 3
(d) 47
(e) 0
Could someone please solve this and provide an explanation?
5 Answers
It could be any of the options.
R = sqrt.(A^2 + B^2 + 2AB*cos(theta))
You can put A and B as 20 and 25 and R as any of the options to find a suitable value of theta.
Hope this helps.
[email protected]
Depending on the direction, you can get a result between -5 and + 45.
Thus 12, 0 and 3 are possible. 50 and 47 are not possible since the maximum magnitude possible for two vectors of 20 and 25 will be 20 + 25 = 45
A vector is a motion that has both size and direction. In this case, we know only the size.
Imagine that are standing in a field and you walk 20 metres in one direction. You then randomly choose another direction and walk 25 metres. Where are you?
It depends entirely on which directions you walked. If you looked this from above, you would walk in one direction for 20 metres and then you have a choice in a circle around this point of where to go next.
It could never be zero, because you walk further the second time than the first, so you can't get back to where you started. It couldn't be 3 either because the closts you can get to where you started is 5 (you walk in one direction then turn round and walk back).
It also can't be 50 or 47 are these are more than the maximum in a straight line (which would be 45).
So the only answer is 12.
The only possible answer is (a) 12.
Think of the magnitudes of the two vectors as two sides of a triangle, and rotate one side with respect to the other. The magnitude of the resultant vector (the remaining side of the triangle) must lie between their difference (5) and their sum (45). Only answer (a), 12, satisfies this condition.
Live long and prosper.
Related Questions
"If this same quantity of energy were transferred to 2.5 kg of water at its boiling point, what fraction of the water wo...
Have you ever noticed how the rear wheel of a bike seems to follow the front wheel closely? Why does this happen, and is...
Find the circumference of a circle with a radius of 5 inches. Please express your answer in terms of pi.
How tall is 77 inches when converted to feet?
Please identify each of the following as measurements: Length Area Volume Mass Density Time Temperature...
In circle O, ST is a diameter. What is the value of x if (2x + 8) equals one of the following options: 22.0, 25.0, 25.4,...
Today's CPUs operate at speeds measured in gigahertz rather than kilohertz. Is this statement true or false?
I have the following mathematical expression: 2 log₂(2) + 2 log₂(6) - log₂(3x) = 3. Is the base indeed 2? I would appr...
I have a question regarding torque in a magnetism context. I understand that the equation τ = IABsin(θ) will be relevant...
Could you please help me find the cube roots of the complex number represented in polar form as 8(cos 216° + i sin 216°)...