Vector question for physics?

Question

If C->(please imagine thats an arrow on top of the C indicating its a vector) is the vector sum of A-> and B->,C->=A-> + B->, what must be true if C=A + B? What must be true if C=0?


Im having some trouble wrapping my head around these kinds of problems, I'm not even quite sure where to start :(

Ahhhh i see! Thanks so much :)

Answer 1

Remember that a vector is both a magnitude and a direction. So in order for the first case to be true C> = A> + B> and C = A + B, A and B must be going in the exact same direction. In order for the second case C> = A> + B> = 0 to be true, A> = -B>, A and B must have the same magnitude and exactly opposite direction.

Answer 2

How do you imagine the vector sum by parallelogram law, triangle law or formula? In all these cases you can see that if vector c = vector a + vector b, then c = 0 implies both a and b are null vectors or a and b have equal magnitude but are oppositely directed making an angle of 180 degrees if drawn from a common initial point

Answer 3

think of of it this way: If I say i want to run at 5 meters according to 2nd, I even have given a value (that's the dimensions, for this reason particularly, the cost). that is often a scalar. yet you don't be attentive to which direction i flow in until I say something like: i want to run 5 meters according to 2nd to the north. here, I particularly supply the cost AND the direction. that is often a vector. a million. rigidity is a vector because of the fact whenever you practice a rigidity to something, you're able to desire to offer it a direction. (If I push down, then the direction is down) 2. bear in mind, there's a distinction between speed and speed. speed is a vector. 3. Temperature isn't a vector because of the fact it does no longer have a direction. 4. Acceleration is a vector. here is an occasion for you: Mass vs weight. Mass is a scalar, weight is a vector! once you're saying this merchandise is 5kg, that's the comparable no rely what direction you supply it. Weight is distinctive because of the fact it refers back to the rigidity that gravity imposes on an merchandise. provided that gravity is a rigidity, that could be a vector quantity.

Answer 4

Think of a vector as a path,like if your were walking through the path in the paper.
C=A + B
Because we have no vectors here it means that C has the size of A (called norm of the vector )plus the size of B.
It means that to follow C, A and B have the same slope and direction.
If C = 0, A->= - B->; following the paths you return to the point from were you started.

Answer 5

Draw A from the origin to some point in sector I. Then draw another vector B anywhere. Now transport the B's tail to the A's head keeping the same slope/direction/length of B. Draw a vector from the origin to the head of B; that will be A+B=C.

Answer 6

if c=a+b then all the vectors have the same direction and orientation;
if c=0 then A-> and B-> (in your notation :-) have equal modulus but opposite direction

Answer 7

C->=A->+B-> means:

Cx = Ax + Bx and Cy = Ay + By

if C->=A->+B-> means that they are like a Tree Angle.
if C->=0 It Means that Ax + Bx = 0 Means Ax = -Bx also Ay = -By