Question

Add vectors A ,B,and Ceach having magnitude of 100 units and inclined to the X axis at angles 45 , 135, and 315 respectively.

Answer 1

SOLUTION::

y component of A vector = 100 sin 45° = 100/√2 unit
y component of B vector = 100 sin 135° = 100/√2 unit
y component of C vector = 100 sin 315° = -100/√2 unit
Resultant of y component = (100/√2 + 100/√2 - 100/√2) unit = 100/√2 unit


x component of A vector = 100 cos 45° = 100/√2 unit
x component of B vector = 100 cos 135° = -100/√2 unit
x component of C vector = 100 cos 315° = 100/√2 unit
Resultant of x component = (100/√2 - 100/√2 + 100/√2) unit = 100/√2 unit


Total resultant of x and y component = √[(100/√2)²+(100/√2)²] = 100

Now,

tan D = (y component/x component) = 1

D = tan⁻¹(1) = 45°

So, the resultant is 100 unit and 45° with x-axis.

hope it helps