Given the points A(2, 2, 1) and B(9, 3, 6) and the plane K: 2x + 6y + 6z - 9=0. Define: a. The equation of the line that passes through A and is perpendicular to the plane K. b. The equation of the plane that passes through the midpoint of the line segment AB and is perpendicular to the line AB.

Q: Find the point, P, at which the line intersects the plane. x= - 3+ 10t, y = 9- 9t, z= 9- 7t; - 10x +…

A: The objective is to find the point of P, at which the line intersects the plane.

Q: b0 = 12, b1 = 0, b2 = -5a. determine whether the plane slopes upward, slopes downward, or is…

A: a).Direction of the slope of a plane:If the sign of the partial slope is positive, the plane slopes…

Q: b0 = -6, b1 = 5, b2 = 0a. determine whether the plane slopes upward, slopes downward, or is…

A: (a)Direction of the slope of a plane:If the sign of a partial slope is positive, the plane slopes…

Q: b0 = –2, b1 = 4, b2 = –7 a. determine whether the plane slopes upward, slopes downward, or is…

A:

Q: b0 = 0, b1 = 0, b2 = 3a. determine whether the plane slopes upward, slopes downward, or is…

A: (a)Direction of the slope of a plane:If the sign of a partial slope is positive, the plane slopes…

Q: b0 = 12, b1 = 0, b22 = −5 a. determine whether the plane slopes upward, slopes downward, or is…

A: The given values are b0 is 12, b1 is 0 and b2 is –5.

Q: b0 = –3, b1 = 4, b2 = 6a. determine whether the plane slopes upward, slopes downward, or is…

A: It is given that the y-intercept and partial slopes of the plane are –3, 4, and 6 respectively.

Q: b0 = 6, b1 = -2, b2 = -1a. determine whether the plane slopes upward, slopes downward, or is…

A: a)Direction of the slope of a plane:If the sign of a partial slope is positive, the plane slopes…

Q: The equation of the plane which is parallel to y -axis and cuts off intercepts of length 2 and 3…

A:

Q: b0 = 5, b1 = 2, b2 = 7a. determine whether the plane slopes upward, slopes downward, or is…

A: (a)Direction of the slope of a plane:If the sign of a partial slope is positive, the plane slopes…

Q: C. Find the equation of the plane passing thru P;(-1,2, –3) and perpendicular to the line through…

A:

Q: b0 = 5, b1 = 2, b2 = 7 a. determine whether the plane slopes upward, slopes downward, or is…

A: a. The y-intercept and partial slopes of the plane are respectively b0=5, b1=2, b2=7. Direction of…

Q: 3) Find equations for the lines: h the no e. The line through (1,1,1) parallel to the z-axis. f. The…

A:

Q: b0 = 0, b1 = −0.05, b2 = 1.5 a. determine whether the plane slopes upward, slopes downward, or is…

A:

Q: b0 = -2, b1 = 3, b2 = -7a. determine whether the plane slopes upward, slopes downward, or is…

A: (a)Direction of the slope of a plane:If the sign of a partial slope is positive, the plane slopes…

Q: b0 = 6, b1 = −2, b2 = −1 a. determine whether the plane slopes upward, slopes downward, or is…

A:

Q: b0 = 12, b1 = 0, b2 = −5 a. determine whether the plane slopes upward, slopes downward, or is…

A:

Q: Find the​ point, P, at which the line intersects the plane. x=-5-6t , y=9-8t , z=8+7t ; 2x-4y-9z=-2…

A:

Q: b0 = −6, b1 = 5, b2 = 0 a. determine whether the plane slopes upward, slopes downward, or is…

A: The given values are b0 = –6, b1 = 5, b2 = 0. Part (a): The coefficient of x2 is b2 and the value of…