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: 1. Find an equation of the plane that contains the line r = -2+ 3t, y = 4+2t, z = 3 - t and is…

A: We have to find

Q: Given = (8,−4,1) + t(4, 4, −2), find the point where the line intersects the plane with equation z +…

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Q: (x = t r:{y = -t (z = 1+ 4t concurrent, and if so, determine the point P common to them. Check if…

A: Let the equation of a line passes through the point x0,y0,z0 with the direction vector v→=l,m,n be…

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…

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Q: Find the intersection of the following geometric objects: the plane 3x + 2y - z = -9 and the line…

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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: Find the equation for the plane through the points Po(-2,3,5), Qo(-4, – 1, - 2), and Ro(4,1,0).

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Q: Q1. Find the point of intersection of the lines L, and Ly whose equations are given as: L₁: (x = 1,…

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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: Find an equation of the line passing through Po and normal to the plane P. Po(2,3,4); P: 3x- 2y +z=…

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

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Q: Find the point of intersection of the line with equation (1,8,3) + t(1,-1,3) and this plane. What is…

A: Now we will find the point of intersection.  And we  will find the y coordinate of this point

Q: Find the equation of the plane through the point (2, 4, 3) that is perpendicular to the line r = (2i…

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Q: Find and describe the intersection of the following line and plane: T:2x+3y-4z =-7 and r = (4,2,5)…

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Q: Find the cartesian equation of the plane determined by the two intersecting lines x-4 y+1 z-2 L1: 3…

A: Here,  v1=3i+2j+kv2=5i+3j+2k v1×v2=ijk321532=i4-3-j6-5+k9-10=i-j-k Thus, the equation of the plane…

Q: Using the following points, find the equation of the plane. Write the equation in standard form…

A: Given, P2p,3q,3Q6p,-3q,1Rp,4q,2 The equation of a plane passing through points P(x1, y1, z1), Q( x2,…

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

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