A vector has x component of -25.0 units and y component of 40.0 units find the magnitude and direction of the vector.

Explanation

Consider a vector `vecA = A_(x)hati + A_(y)hatj`
`therefore vecA =-25hati + 40hatj`
`|vecA| = sqrt(A_(x)^(2) + A_(y)^(2)) =sqrt((-25.0)^(2) + (40.0)^(2))`
`=47.16 = 47.2` units
and `tan alpha = A_(y)/A_(x) = 40.0/(-25.0) = 1.6`
`therefore alpha =tan^(-1) (-1.6) =-58.0^(@)` with `-ve` x-axis
This is equivalent to (122°) in anticlockwise direction with the x - axis.