2. Find angle(A,B)
`A=(3,4)`,`B=(4,3)`
Solution:
Here `vec A=(3,4),vec B=(4,3),vec C=(3,4)`
The angle between two vectors `vec A` and `vec B` is given by
`cos(theta)=(vec A * vec B)/(|vec A| * |vec B|)`
1. Calculate dot product
`vec A * vec B`
`=A_1*B_1 + A_2*B_2`
`=3*4 + 4*3`
`=12 + 12`
`=24`
2. Calculate magnitude of vectors
`|vec A|`
`=sqrt(A_1^2 + A_2^2)`
`=sqrt(3^2 + 4^2)`
`=sqrt(9 + 16)`
`=sqrt(25)`
`=5`
`|vec B|`
`=sqrt(B_1^2 + B_2^2)`
`=sqrt(4^2 + 3^2)`
`=sqrt(16 + 9)`
`=sqrt(25)`
`=5`
3. Calculate angle between vectors
`cos(theta)=(24)/(5 * 5)=0.96`
`:. theta=cos^(-1)(0.96)=0.2838` rad
`:. theta=16.2602 ^circ`
This material is intended as a summary. Use your textbook for detail explanation.
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