Question

Three forces A = (i + j + k), B = (2i - j + 3k), and (' arc acting on a body which is kept at equilibrium. Find C

Answer 1

Given:

Three force A, B and C are acting on body. Body is in equilibrium condition.

To Find:

What is value of force C ?

Solution:

Value of first and second force:

$\mathbf{First\ force = A = \hat{i}+\hat{j}+\hat{k}}$

$\mathbf{Second\ force = B = 2\hat{i}-\hat{j}+3\hat{k}}$

Third force = C = Unknown

We know that when body is in equilibrium condition, net force acting on body is zero,means:

$\mathbf{\sum F=0}$

This can be written as:

$\mathbf{A+B+C=0}$

On putting respective value in above equation:

$\mathbf{\hat{i}+\hat{j}+\hat{k}+2\hat{i}-\hat{j}+3\hat{k}+C=0}$

On simplify:

$\mathbf{3\hat{i}+4\hat{k}+C=0}$

So:

$\mathbf{C=-3\hat{i}-4\hat{k}}$

Means value of third force C is $\mathbf{-3\hat{i}-4\hat{k}}$

Answer 2

hope this helps you

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