A vector of magnitude 20 is added to a vector of magnitude 25. The magnitude of this sum might be...?

Question

(a)12 (b)50 (c)3 (d)47 (e)0
Could anyone solve this? explain please

Answer 1

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.

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Answer 2

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

Answer 3

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.

Answer 4

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.

Answer 5

12