The angle between the two vectors is 126° 52' 11".
The given parameters;
vector A = 3.00i + 1.00j
vector B = 1.00i + 3.00j
The angle between the two vectors is calculated as follows;
The dot product of vectors A and B is calculated as;
A.B = ( 3i + 1j ) . ( 1i +3j )
= ( 3 × 1 ) + ( 1 × 3 )
= 3 + 3
= 6
The magnitude of vectors A and B is calculated as;
|A| = ![\sqrt[]{3^2 + 1^2} = \sqrt[]{10} \\](https://tex.z-dn.net/?f=%5Csqrt%5B%5D%7B3%5E2%20%2B%201%5E2%7D%20%3D%20%5Csqrt%5B%5D%7B10%7D%20%5C%5C)
|B| = ![\sqrt[]{1^2 + 3^2} = \sqrt[]{10} \\](https://tex.z-dn.net/?f=%5Csqrt%5B%5D%7B1%5E2%20%2B%203%5E2%7D%20%3D%20%5Csqrt%5B%5D%7B10%7D%20%5C%5C)
The angle between in two vectors is calculated as;
![Cos \theta = \frac{6}{\sqrt[]{10}\sqrt[]{10} } \\\\Cos \theta = \frac{6}{\ 10 }\\\\Cos \theta = 0.6\\\\\theta = cos^-^1 (0.6)\\\\\theta = 126\\](https://tex.z-dn.net/?f=Cos%20%5Ctheta%20%3D%20%5Cfrac%7B6%7D%7B%5Csqrt%5B%5D%7B10%7D%5Csqrt%5B%5D%7B10%7D%20%20%7D%20%5C%5C%5C%5CCos%20%5Ctheta%20%3D%20%5Cfrac%7B6%7D%7B%5C%2010%20%7D%5C%5C%5C%5CCos%20%5Ctheta%20%3D%200.6%5C%5C%5C%5C%5Ctheta%20%3D%20cos%5E-%5E1%20%280.6%29%5C%5C%5C%5C%5Ctheta%20%3D%20126%5C%5C)
Therefore, the angle between the two vectors is 126° 52' 11".
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The last one, Tension = 30N, Normal force = 20 N
Answer:
4. The equilibrium will shift to favor formation of NO2(g)
Explanation:
According to La Chatalier's Principle which states that when an equilibrium system undergoes changes either in temperature, volume or concentration; there will be in a change in the system in order to reach equilibrium.
From the above equation,
N2O4(g) ⇀↽ 2 NO2(g)
From the above reaction, there are 2 moles of gaseous product on the left and 1 mole of gaseous reactant.
Therefore, there are more moles of gases in the left hand side than the right hand side.
Because a decrease in volume favors the direction that produces fewer moles, an increase in volume will therefore shift this system towards the side with more moles of gases that is, more products are formed hence, this system will shift to right and produce more moles of products i.e more NO2(g) formed.
Answer: Power is 200 W
Explanation: Power P = work done / time used.
P = W/t = mgh/t = 154 kg · 9.81 m/s²· 4 m / 30 s = 201 W
