Question

Find the angle between each of the following pairs of vectors A⃗ =Axi^+Ayj^A→=Axi^+Ayj^ and B⃗ =Bxi^+Byj^B→=Bxi^+Byj^.

Ax1=Ax1= -1.00, Ay1=Ay1= 5.80; Bx1=Bx1= 1.00, By1=By1= -2.30.

Ax2=Ax2= 3.60, Ay2=Ay2= 5.40; Bx2=Bx2= 11.0, By2=By2= 5.60.

Ax3=Ax3= -4.00, Ay3=Ay3= 2.00; Bx3=Bx3= 7.00, By3=By3= 14.00.

Answer 1

Two Vectors and can be multiplied in two different ways

1. Dot product:

2. Cross product:

where and are the magnitudes of the vectors and . is the angle between the vectors   and and is the unit vector in the dierction perpendicular to both and .

From definition it can be see that the result of dot product is a scalar and that of cross product is a vector.

If a vector   can be written in its component form;  , where and are the unit vectors along X,Y and Z directions, then

Also the dot product between two vectors   and can be written as

But fro the definition

Therefore we can write and

Here in the question both  

therefore

• If Ax= -1.00, Ay= 5.80; Bx= 1.00, By= -2.30. Then

Similarly

• If Ax= 3.60, Ay= 5.40; Bx= 11.0, By= 5.60. Then

• If Ax= -4.00, Ay= 2.00; Bx3= 7.00, By= 14.00. Then