Question

1.
Three concurrent co-planar forces 1 N, 2 N and
3 N acting along different directions on a body
a) can keep the body in equilibrium if 2 N
and 3 N act at right angle.
b) can keep the body in equilibrium if 1 N
and 2 N act at right angle.
cannot keep the body in equilibrium.
can keep the body in equilibrium if 1 N
and 3 N act an acute angle.​

Answer 1

Given:

Three concurrent co-planar forces 1 N, 2 N and 3 N acting along different directions on a body.

To find:

Whether these force vectors can keep a body in equilibrium.

Calculation:

According to Triangle Law of Vector, 3 vectors can be in equilibrium only when they can form triangle.

Also , the pre-requisite for triangle construction is that :

SUM OF TWO SIDES OF THE TRIANGLE WILL ALWAYS BE GREATER THAN THE THIRD SIDE.

In this case , we have three vectors with magnitude 1N , 2N and 3N.

Let's see the following cases :

$1) \: 2N + 3N > 1N$

$2) \: 1N + 3N > 2N$

$3) \: 1N + 2N = 3N$

In the 3rd case , we can see that sum of two vectors is equal to the third vector. Hence triangle construction fails.

So these forces can't keep a body in equilibrium.

Statement 3 is correct