Find the angle between each of the following pairs of vectors \vec{A}=A_x\hat{i}+A_y\hat{j} and \vec{B}=B_x\hat{i}+B_y\hat{j} A_{x_1}=-2.20,\ A_{y_1}=6.60\ B_{x_1}=2.00,\ B_{y_1}=-2.30

Cabiolab

Cabiolab

Answered question

2021-05-23

Find the angle between each of the following pairs of vectors A=Axi^+Ayj^ and B=Bxi^+Byj^
Ax1=2.20, Ay1=6.60 Bx1=2.00, By1=2.30

Answer & Explanation

i1ziZ

i1ziZ

Skilled2021-05-24Added 92 answers

The expression for the vector form of A is,
A=Axi^+Ayj^
The expression for the vector form of B is,
B=Bxi^+Byj^
The expression for the magnitude of the vector A is,
|A|=Ax2+Ay2
The expression for the magnitude of the vector B is,
|B|=Bx2+By2
The vector form of the A2 is,
A1=Ax,1i^+Ay,1j^
=(2.20)i^+(6.60)j^
=(2.20)i^+(6.60)j^
The vector form of B2 is,
B2=Bx,2i^+By,2j^
=(11.8)i^+(6.80)j^
The expression for the dot product of the vectors A2 and B2 is,
A2B2=|A1||B1|cosθA1B1
θA2B2=cos1(AB|A2||B2)
=cos1(((2.20)i^+(6.60)j^)((2.00)i^(2.30)j^)((2.20)2+(6.60)2)((2.00)2+(2.30)2))
=22.57

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