Question

add vectors A,B and C each having magnitude of 100 units and inclined to the x- axis at angles 45 degree, 135degree, 315degree respectively.

Answer 1

Sol. x component of
A ⃗ = 100 cos 45° = 100 / √2 unit
x component of B ⃗ = 100 cos 135° = 100 / √2
x component of C ⃗ = 100 cos 315° 100 / √2
Resultant x component = 100 / √2 – 100 / √2 + 100/ √2 = 100 √2
Y component of A ⃗ = 100 sin 45° = 100 / √2 unit
Y component of B ⃗ = 100 sin 135° = 100 / √2
Y component of C ⃗ = 100 sin 315° = 100 / √2
Resultant y component = 100 / √2 + 100 / √2 + 100 / √2 – 100 / √2 = 100 / √2 Resultant = 100 Tan α (y component )/(x component ) = 1 ⇒ α = tan-1 (1) = 45°
The resultant is 100 unit at 45° with x-axis.