Help with adding vectors (10 points up for grabs)?

Question

Vector 1 goes 8m south.

Vector 2 goes 12m east.

Vector 1's head joins on to Vector 2's tail.

The unknown Vector (x) joins from Vector 1's tail to Vector 2's head thus creating a right-angled triangle. How do i find the displacement and distance of the unknown vector (x)???

Answer 1

You need to draw it out. Draw a scale diagram, or if you don' want to, just a rough diagram to visualize the two vectors. Vector (x) is the resultant force, the result of the two previous vectors. So you see you actually form a right angled triangle with the right angle at the turning and the resultant force being the hypotenuse. Using Pythagoras theorem, you get (x) = sqrt (8^2+12^2). So the answer is approximately 14.4. This is the length of the vector, or the displacement. Distance is a scalar quantity, so it is the total distance of the path taken, that is 8+12=20.

Answer 2

distance is just to add the two distances> 8m+12m

distance = 20m

to find displacement, do the Polygon method(head to tail).

graph 8m and 12m on the coordinate plane, then connect the two arrow heads. solve for the hypotenuse (slanting line) using the pythagorean theorem c^2=a^2+b^2.

(for more info, give me your email add and ill send an illustration to you).

best answer please? :D

Answer 3

You just add the two vectors together.

You can break them down to x and y parts and add them. But this is a simpler case since the two vectors are at right angles. Just use trig.

magnitude of x = √(8² + 12²) = 14.42 m, which is also the distance.

angle of x = arc tan 8/12 = 33.7 degrees, negative from the x axis.

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