Question

Vector A has magnitude of 8.0 at an angle of 20.0deg from the x-axis. Vector B has magnitude of 7.0 at an angle of -10.0 deg from the x-axis. Let C=A+B. Let D=A-B. Let V=2*A-B.

1.What is the x-component of vector C?

2.What is the y-component of vector C?

3.What is the x-component of vector D?

4.What is the y-component of vector D?

5.What is the x-component of vector V?

6.What is the y-component of vector V?

Answer 1

A = 8*cos20 i^ + 8*sin20 j^ = 7.52 i^ + 2.74 j^

B = 7*cos10 i^ - 7*sin10 j^ = 6.9 i^ - 1.22 j^

C = A + B = (7.52 + 6.9) i^ + (2.74 - 1.22) j^ = 14.42 i^ + 1.52 j^

D = A - B = (7.52 - 6.9) i^ + (2.74 + 1.22) j^ = 0.62 i^ + 3.96 j^

V = 2A - B = 2*(7.52 i^ + 2.74 j^) - (6.9 i^ - 1.22 j^) = 8.14 i^ + 6.7 j^

1) the x-component of vector C = 14.42

2) The y-component of vector C = 1.52

3) x-component of vector D = 0.62

4) y-component of vector D = 3.96

5) x-component of vector V = 8.14

6) y-component of vector V = 6.7