Question

Three vectors A, B and Care as shown in figure.
If magnitude of A is 4 m and A+B+C =0, then
the magnitudes of B and C are respectively

(1) 4 m, 4 m
(2) 4/3 m, 43 m
(4) 4/3m, 4m
(3) 4m, 43 m​

Answer 1

Answer:

I think the answer will be the second option

Answer 2

So the resultant of the three vectors A, B and C is 0.

Then we can have the resultant of their horizontal components (x - components) 0, i.e.,

A cos 0° + C sin 30° - B cos 30° = 0

=> B√3 / 2 - C / 2 = 4

=> B√3 - C = 8 → (1)

And also the resultant of their vertical components (y - components) 0, i.e.,

A cos 90° - B sin 30° + C cos 30° = 0

=> C√3 = B → (2)

So, from (2), (1) becomes,

2C = 8

=> C = 4 m

And (2) becomes,

B = 4√3 m

Hence option (4) is the answer.