Answer:
The vector equation of the line is

Parametric equations for given line are

Explanation:
The vector equation of the line is given by

r₀ = (7, -8, 3)
v = (1, 6, -13)
At these points the vector equation for this line is:

Parametric equations for given line are

Answer:
V₂= 1 L
Explanation:
Given that
Volume occupies V₁= 6 L
Initial pressure = P₁
Initial temperature = T₁
The final pressure =P₂ = 2 P₁
Final volume =V₂
Final temperature = T₁/3
As we know that equation for ideal gas
P V = m R T
P=pressure, V=volume, T=temperature
m=mass ,R=gas constant
Now from mass conservation



6 = 3 x 2 V₂
V₂= 1 L
So the final volume will be 1 L
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Answer:
2.06 m/s
Explanation:
From the law of conservation of linear momentum, the sum of momentum before and after collision are equal. Considering this case where we have frictionless surface, no momentum is lost in the process.
Momentum before collision
Momentum is given by p=mv where m and v represent mass. The initial sum of momentum will be 9v+(27*0.5)=9v+13.5
Momentum after collision
The momentum after collision will be given by (9+27)*0.9=32.4
Relating the two then 9v+13.5=32.4
9v=18.5
V=2.055555555555555555555555555555555555555 m/s
Rounded off, v is approximately 2.06 m/s