Question

An object is acted upon by the forces F1equalsleft angle12​,7​,2right angle and F2equalsleft angle0​,4​,8right angle. Find the force F3 that must act on the object so that the sum of the forces is zero.

Answer 1

`F_3=(-12,-11,-10)`

Step-by-step explanation:

It is given that,

Force,
`F_1=(12,7,2)`

Force,
`F_2=(0,4,8)`

We need to find the force F₃ that must act on the object so that the sum of the forces is zero. Let
`F_3=(x,y,z)`

According to question,
`F_1+F_2+F_3=0`

`(12,7,2)+(0,4,8)+(x,y,z)=0`

`(12+x)+(11+y)+(10+z)=0`

Since, 12 + x = 0, 11 + y = 0 and 10 + z = 0

The third force is equal to,

`F_3=(-12,-11,-10)`

Hence, this is the required solution.