Answer:
a) < 3 , -4 >
b) < 3 , -4 >
Explanation:
a) If you can imagine this, adding vectors is like putting them "tip to tail", where you put the beginning point of vector B to the end point of vector A (or vice versa). Your new vector (A+B) would be from the "tip" of vector A to the "tail" of vector B.
Mathematically, this is the same as adding the x-components of each vector together as well as the y-components.
Vector A: 3 units along the positive x-axis: < 3 , 0 >
Vector B: 4 units along the negative y-axis: < 0 , -4 >
A+B = < 3 , 0 > + < 0 , -4 > = < (3+0) , (0+(-4)) > = < 3 , -4 >
b) Subtracting is like adding a negative, so you could use the same "tip to tail" visual by adding the negative of vector B instead (which is B in the opposite direction).
Vector A: < 3 , 0 >
Vector B: < 0 , -4 >
Vector -B: < 0 , 4 >
A-B = A+(-B) = < 3 , 0 > + < 0 , 4 > = < (3+0) , (0+4) > = < 3 , 4 >
