If `vecA=3hati+4hatj` and `vecB=7hati+24hatj`, find a vector having the same magnitude as `vecB` and parallel and same direction as `vecA`.

Answer

`15hati + 20 hatj`

Explanation

`" "vecA = 3hati + 4hatj`
`" "vecB = 7hati + 24hatj`
Let `vecC` parallel to `vecA` and its magnitude is equal to `vecB`, then
`" "vecC = xhati + yhatj` (say )
Also, `" "(x)/(3) = (y)/(4)`
`rArr " "x=(3)/(4)y" "(vecA||vecC)" ".....(i)`
Now, `|vecC|= |vecB|`
`" "sqrt(x^(2) + y^(2)) = sqrt(24^(2) + 7^(2))`
`" "sqrt((9)/(16)y^(2) + y^(2)) = 25`
`" "sqrt((25)/(16)y^(2) )=25`
` rArr " "(5)/(4)y = 25`
`" "7 = 20` Now, `x = (3)/(4) = 15`
So, `vecC = 15hati + 20 hatj`