Question

3. Add vectors A, B and C each having magnitude of 100
unit and inclined to the X-axis at angles 45°, 135º and
315º 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.