Question

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

Concept of Physics - 1 , HC VERMA , Chapter - "Physics and Mathematics"

Answer 1

Thanks for asking the question!

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.

Answer 2

Components of vector A along s and y axis are:-

100 × cos(45°) = 70.71 N and

100 × sin (45°) = 70.71 N

Components of vector B along x and y axis are:-

100 × cos(135°) = −70.71 N and

100 × sin(135°) = 70.71 N

Components of vector C along x and y axis are:-
100 × cos(315°) = 70.71 N and 

100 × sin(315°) = −70.71N

So the components of resultant vector along x and y axis are:-

70.71 − 70.71 + 70.71 = 70.71 N and 70.71+70.71−70.71=70.71 N.

So the magnitude is root 70.712+70.712 bar = 100 N and angle is tan −1(70.7170.71) = 45° from x axis.