Find an equation of the plane. the plane that passes through the point (3, 4, 5) and contains the line x = 5t, y = 3 + t, z = 4 − t

Hence the equation of plane is  x-4y+z+8=0

Explanation:

Since the points (3,4,5) and (0,3,4) are on the same plane

Now,

the vector a using two points (5,4,3) and (0,3,4) will be < -5,1,1>

and the vector b using points (5,4,3)and (3,4,5)  will be <-2,0,2>

Now, n=a×b

Normal vector (n)

n =-2i+8j-2k

Now the general equation of  plane:

Equation of plane:

Hence the equation of plane is x-4y+z+8=0

answer: sine

step-by-step explanation:

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step-by-step explanation: