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

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.

38.6°

step-by-step explanation:

resultant is 10 pound

smaller force = 8 pound

angle formed = tan⁻¹(

                        =tan⁻¹(

                          =tan⁻¹(0.8)

                        =38.6°