Vector A has a magnitude of 6.40 units and makes an angle of 30.0

A = 6.4 ( cos 30 i + sin 30 j ) = 5.542 i + 3.2 j

B = 6.4 ( -i )

a)

A + B = -0.857 i + 3.2 j

A - B = 11.942 i + 3.2 j

A+B form an equivalent triangle and resultant R is 6.40 units

A = 6.4 ( cos 30 i + sin 30 j ) = 5.542 i + 3.2 j

B = 6.4 ( -i )

a)

A + B = -0.857 i + 3.2 j

Magnitude = sqrt ( 0.857^2 + 3.2^2) = 3.312 units

Direction = 105 degrees with positive x axis

A - B = 11.942 i + 3.2 j

Magnitude = sqrt ( 11.942 ^2 + 3.2^2) = 12.3633 units

Direction = tan^-1 ( 3.2/11.942) = 15 degrees with positive x axis

The component of A along X axis is A_x = 6.4cos(30^o) i = 5.54 i

The component of B along X axis is B_x = 6.4cos(-180^o) i = -6.4 i

The component of A+B along X axis is A_x + B_x = -0.86 i

The component of A-B along X axis is A_x - B_x = 11.94 i

The y component of A is A_y = 6.4sin(30^o) j =3.2 j

The y component of B is B_y = 6.4sin(180^o) = 0 j

The y component of A+B is A_y + B_y = 3.2 j

The y component of A-B is A_y - B_y = 3.2 j

So A+B = -0.86 i + 3.2 j

A-B = 11.94 i + 3.2 j

the vector sum is

A + B = (Ax + Ay) + (Bx + By)

where Ax = 6.40 x cos(30o),Ay = 6.40 x sin(30o),Bx = 6.40 x cos(180o) and By = 6.40 x sin(180o)

similarly the vector difference