Vector A has a magnitude of 6.0 m and points 30° north of east. Vector B has a magnitude of 4.0 m and points 30° west of north. The resultant vector A + B is given by:

(a) 9.8 m at an angle of 26° north of east,

(b) 3.3 m at an angle of 26° north of east,

(c) 7.2 m at an angle of 26° east of north,

(d) 3.3 m at an angle of 64° east of north or

(e) 9.8 m at an angle of 64° east of north

The resultant vector A + B is given by 7.2 m at an angle of 26° east of north,

C

Explanation:

Resolving the vectors to vertical and horizontal component;

Vertical;

Vector A = 6sin30

Vector B = 4sin60

Resultant vertical = 6sin30 + 4sin60 = 6.464m

Horizontal;

Vector A = 6cos30

Vector B = -4cos60

Resultant horizontal = 6cos30 - 4cos60 = 3.196m

Resultant R = √(6.464^2 + 3.196^2) = 7.2m

Tanθ = 6.464/3.196

θ = taninverse (6.464/3.196) BN

θ = 64° north of East.

Or

26° east of north

The resultant vector A + B is given by 7.2 m at an angle of 26° east of north,

The resultant vector A + B is given by 7.2 m at an angle of 26° east of north. Hence, option (c) is correct.

Given data:

The magnitude of vector A is, A = 6.0 m.

The direction of vector A is, 30° north of east.

The magnitude of vector B is, B = 4.0 m.

The direction of vector B is, 30° west of north.

The quantity having both the magnitude as well as the magnitude are known as vector quantities.

Resolving the vectors to vertical and horizontal component;

Along the Vertical direction;

Vector A = 6sin30

Vector B = 4sin60

Resultant vertical vector = 6sin30 + 4sin60 = 6.464 m

Along the Horizontal direction;

Vector A = 6cos30

Vector B = -4cos60

Resultant horizontal vector = 6cos30 - 4cos60 = 3.196 m

Now, the resultant vector is calculated as,

And the resultant direction of vectors is,

( North of East)

θ = 64° north of East.

Or

26° east of north

Thus, we can conclude that the  resultant vector A + B is given by 7.2 m at an angle of 26° east of north. Hence, option (c) is correct.

Learn more about the vector quantities here:

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