1.

Find the component of a vector ` vec A = 3 hat I + 4 hat j` along the direction of ` 2hat I -3 hat j`.

Answer» Here, `vec A =(3 hat I + 4 hat j ), vec B =( 2hat I - 3 hat j)`
Unit vector ob ` vec B` ,
` hat B (vec B) /B = (2 hai -3 hat j)/( sqrt( (2)^(2) + (-3)^(2)) =(2 hat - 3 hat j)/(sqrt 13)`
Let `theta` be the anle between ` vec A and vec B`. The
componet of `vec A` along the direction of ` vec B` is
`=(A cos rhea ) hat B = (vec A . hat B) hat B`
`=[(3 hat i + 4 hat j). ((2 hati -3 hat j)/(sqrt 13))] ((2 hat i -3 hatj )/(sqrt 13 ))`
`((6 -12))/(13) (2 hat i -3 hat j) =- 6/(13) (2 hat i -3 hat j)`.


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