Answer:
Explanation:
To find the point of intersection between the line and the plane, we need to substitute the parametric equations of the line into the equation of the plane and solve for the values of the parameters. The parametric equations of the line are given as:
x−4 ÷ 4 = y+3 ÷ 2 = z ÷ −1
And the equation of the plane is:
7x −y + z = 9
We can use the first two parametric equations to express x and y in terms of z:
x−4 ÷ 4 = y+3 ÷ 2 = z ÷ −1 = t (where t is a parameter)
From the first equation, we have:
x − 4= 4t
x = 4t + 4
From the second equation, we have:
y + 3 = 2t
y = 2t− 3
Now, substitute these expressions for x and y into the equation of the plane:
7x − y + z = 9
7(4t+4)−(2t−3)+z=9
Simplify the equation:
28t + 28 − 2t + 3 + z = 9
Combine like terms:
26t + z + 28 + 3 = 9
26t + z + 31 = 9
Subtract 31 from both sides:
26t + z = −22
Now, we have a system of two equations:
x =4t + 4
y = 2t − 3
26t + z = −22
We can solve this system to find the values of t and z. Once we have those values, we can substitute them into the expressions for x and y to find the point of intersection.