Question

The resultant of two vectors of magnitude 2 and 3 is 1the angle between them is?

Answer 1

`180^@`

Explanation:

From parellelogram law of vectors magnitude of resultant vector `("R")` is given by the fromula

`"R" = sqrt("A"^2 + "B"^2 + "2AB"cos(θ))`

`1 = sqrt[2^2 + 3^2 + (2 × 2 × 3 × costheta)]`

Squaring on both sides

`1^2 = 2^2 + 3^2 + (2 × 2 × 3 × costheta)`

`1 - (4 + 9) = 12costheta`

`-cancel(12) = cancel(12)costheta`

`θ = cos^-1(-1) = color(Green)180^@`

If `"3 N"` is acted along +ve x-axis and `"2 N"` along -ve x-axis then resultant force is `"1 N"` along +ve x-axis.